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Filed Pursuant to Rule 424(b)(5)

Registration No. 333-251172

The information in this preliminary prospectus supplement is not complete and may be changed. A registration statement relating to these securities has become effective. This preliminary prospectus supplement and the accompanying prospectus are not an offer to sell these securities, and we are not soliciting offers to buy these securities, in any state or other jurisdiction where the offer or sale is not permitted.

SUBJECT TO COMPLETION, DATED DECEMBER 7, 2020

PRELIMINARY PROSPECTUS SUPPLEMENT (To Prospectus dated December 7, 2020)

$200,000,000

Common Stock

We are offering $200,000,000 of shares of our common stock. Our common stock is listed on the Nasdaq Global Select Market under the symbol "KURA." On December 4, 2020, the last sale price of our common stock as reported on the Nasdaq Global Select Market was $36.80 per share.

Investing in our common stock involves significant risks. Please read "Risk Factors" on page S-6 of this prospectus supplement and the documents incorporated by reference into this prospectus supplement.

Per

Total

Share

Public offering price

$

$

Underwriting discounts and commissions(1)

$

$

Proceeds, before expenses, to us

$

$

  1. See "Underwriting" for a description of the compensation payable to the underwriters.

We have granted the underwriters an option to purchase up to an additional $30,000,000 of shares at the public offering price, less the underwriting discounts and commissions, for a period of 30 days following the date of this prospectus supplement. If the underwriters exercise in full their option, the

total underwriting discounts and commissions payable by us will be $

, and the total proceeds to us, before expenses, will be $

.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved these securities or determined if this prospectus supplement or the accompanying prospectus is accurate or complete. Any representation to the contrary is a criminal offense.

The underwriters expect to deliver the shares to purchasers on or before December , 2020.

Joint Bookrunning Managers

SVB Leerink

Credit Suisse

Barclays

Stifel

Prospectus Supplement dated December , 2020

Table of Contents

TABLE OF CONTENTS

Prospectus Supplement

ABOUT THIS PROSPECTUS SUPPLEMENT

Page

S-1

PROSPECTUS SUPPLEMENT SUMMARY

S-2

RISK FACTORS

S-6

SPECIAL NOTE REGARDING FORWARD-LOOKING STATEMENTS

S-7

USE OF PROCEEDS

S-9

DILUTION

S-10

UNDERWRITING

S-11

LEGAL MATTERS

S-18

EXPERTS

S-18

WHERE YOU CAN FIND MORE INFORMATION

S-18

INCORPORATION OF CERTAIN INFORMATION BY REFERENCE

S-19

Prospectus

Page

ABOUT THIS PROSPECTUS

1

SUMMARY

2

RISK FACTORS

7

SPECIAL NOTE REGARDING FORWARD-LOOKING STATEMENTS

8

USE OF PROCEEDS

9

DESCRIPTION OF CAPITAL STOCK

10

DESCRIPTION OF DEBT SECURITIES

15

DESCRIPTION OF WARRANTS

22

LEGAL OWNERSHIP OF SECURITIES

25

PLAN OF DISTRIBUTION

29

LEGAL MATTERS

31

EXPERTS

31

WHERE YOU CAN FIND MORE INFORMATION

31

INCORPORATION OF CERTAIN INFORMATION BY REFERENCE

32

DISCLOSURE OF COMMISSION'S POSITION ON INDEMNIFICATION FOR SECURITIES ACT LIABILITY

33

We have not, and the underwriters have not, authorized anyone to provide you with different information than that which is contained in or incorporated by reference in this prospectus supplement, the accompanying prospectus and in any free writing prospectus that we have authorized for use in connection with this offering. We are not, and the underwriters are not, making an offer to sell these securities in any jurisdiction where the offer or sale is not permitted. You should assume that the information appearing in this prospectus supplement, the accompanying prospectus, the documents incorporated by reference into this prospectus supplement and the accompanying prospectus, and in any free writing prospectus that we have authorized for use in connection with this offering, is accurate only as of the date of those respective documents. Our business, financial condition, results of operations and prospects may have changed since those dates. You should read this prospectus supplement, the accompanying prospectus, the documents incorporated by reference into this prospectus supplement and the accompanying prospectus, and any free writing prospectus that we have authorized for use in connection with this offering, in their entirety before making an investment decision. You should also read and consider the information in the documents to which we have referred you in the sections of this prospectus supplement entitled "Where You Can Find More Information" and "Incorporation of Certain Information by Reference."

S-i

Table of Contents

ABOUT THIS PROSPECTUS SUPPLEMENT

This document is in two parts. The first part is this prospectus supplement, which describes the terms of this offering of common stock and also adds to and updates information contained in the accompanying prospectus and the documents incorporated by reference into this prospectus supplement and the accompanying prospectus. The second part, the accompanying prospectus dated December 7, 2020, including the documents incorporated by reference therein, provides more general information. Generally, when we refer to this prospectus, we are referring to both parts of this document combined. To the extent there is a conflict between the information contained in this prospectus supplement, on the one hand, and the information contained in the accompanying prospectus or in any document incorporated by reference that was filed with the Securities and Exchange Commission, or SEC, before the date of this prospectus supplement, on the other hand, you should rely on the information in this prospectus supplement. If any statement in one of these documents is inconsistent with a statement in another document having a later date-for example, a document incorporated by reference into this prospectus supplement or the accompanying prospectus-the statement in the document having the later date modifies or supersedes the earlier statement. You should assume that the information contained in this prospectus supplement is accurate as of the date on the front cover of this prospectus supplement only and that any information we have incorporated by reference or included in the accompanying prospectus is accurate only as of the date given in the document incorporated by reference or as of the date of the prospectus, as applicable, regardless of the time of delivery of this prospectus supplement or the accompanying prospectus or any sale of our common stock. Our business, financial condition, results of operations and prospects may have changed since that date.

In this prospectus supplement, unless otherwise stated or the context otherwise requires, the terms "Kura," the "Company," "we," "us" and "our" refer to Kura Oncology, Inc.

S-1

Table of Contents

PROSPECTUS SUPPLEMENT SUMMARY

This summary highlights selected information contained elsewhere or incorporated by reference in this prospectus supplement and the accompanying prospectus. This summary does not contain all the information you should consider before investing in our common stock. You should read and consider carefully the more detailed information in this prospectus supplement and the accompanying prospectus, including the factors described under the heading "Risk Factors" in this prospectus supplement on page S-6 and the financial and other information contained in or incorporated by reference into this prospectus supplement and the accompanying prospectus, as well as the information included in any free writing prospectus that we have authorized for use in connection with this offering, before making an investment decision.

Overview

We are a clinical-stage biopharmaceutical company committed to realizing the promise of precision medicines for the treatment of cancer. Our pipeline consists of small molecule product candidates that target cancer signaling pathways where there is a strong scientific and clinical rationale to improve outcomes, and we intend to pair them with molecular or cellular diagnostics to identify those patients most likely to respond to treatment. We plan to advance our product candidates through a combination of internal development and strategic partnerships while maintaining significant development and commercial rights. We presently have two key product candidates in clinical trials, tipifarnib and KO-539.

Tipifarnib is a potent, selective and orally bioavailable inhibitor of farnesyl transferase that has been previously studied in more than 5,000 cancer patients and demonstrated compelling and durable anti-cancer activity in certain patients with a manageable side effect profile. We are currently evaluating tipifarnib in multiple solid tumor and hematologic indications.

Our most advanced solid tumor indication for tipifarnib is in patients with head and neck squamous cell carcinoma, or HNSCC, that carry mutations in the HRAS gene. We are currently conducting a global, multi-center,open-label,non-comparativeregistration-directed clinical trial of tipifarnib in HRAS mutant HNSCC designed with two cohorts: a treatment cohort, which we call AIM-HN, and a prospective observational cohort.

On July 6, 2020, we amended the AIM-HN trial protocol to enable enrollment of patients with any HRAS mutation in addition to patients with a high HRAS variant allele frequency in order to assess the potential for clinical benefit in the overall HRAS mutant HNSCC population, which increased the number of evaluable HNSCC patients for AIM-HN. As a result of the COVID-19 pandemic and the additional patients required for the trial, we anticipate we will face delays in our timelines and milestones for the AIM-HN trial and, accordingly, are unable to reasonably forecast at this time when our AIM-HN trial will become fully enrolled.

In addition to studying tipifarnib in recurrent or metastatic HRAS mutant HNSCC as a monotherapy, we are also examining the potential use of tipifarnib in combination with other oncology therapies to address larger patient populations and pursue earlier lines of therapy. In particular, we are increasingly interested in HNSCC patients whose tumors are dependent on HRAS and/or PI3 kinase alpha, as evidenced by overexpression of the HRAS protein, or PIK3CA mutation or amplification. HRAS and PI3 kinase alpha are believed to be "co-dependent" oncoproteins in HNSCC. Our preclinical data support that notion and suggest that a combination approach has the potential to provide superior antitumor activity relative to inhibiting either target alone. Based upon the unmet need and our encouraging preclinical data, we are prioritizing the clinical development of tipifarnib in combination with a PI3 kinase alpha inhibitor as a strategy to treat both HRAS-dependent and PI3K alpha-dependent HNSCC patients.

S-2

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Kura Oncology Inc. published this content on 07 December 2020 and is solely responsible for the information contained therein. Distributed by Public, unedited and unaltered, on 07 December 2020 21:34:02 UTC