The record settlement with the bank, which was reached in November, does not release JPMorgan from potential criminal liability over the mortgages it packaged into bonds.
But Better Markets said it was still appalled that the settlement gave the bank "blanket civil immunity" for its conduct without sufficient judicial review.
"The Wall Street bailouts were bad enough, but now taxpayers are being forced to accept a secretive backroom deal that may well have been another sweetheart deal," said Dennis Kelleher, the chief executive of Better Markets.
"The Justice Department cannot act as prosecutor, jury and judge and extract $13 billion in exchange for blanket civil immunity to the largest, richest, most politically connected bank on Wall Street."
Better Markets was founded in 2010 to advocate for tough Wall Street reforms.
The lawsuit, which names both the Justice Department and Attorney General Eric Holder, was filed in federal court in Washington.
Better Markets is seeking to have the court prevent the Justice Department from enforcing the settlement until a judge reviews it.
A spokeswoman for the Justice Department could not be immediately reached for comment. A JPMorgan spokeswoman declined to comment on the lawsuit.
Lawmakers and others have criticized the Obama administration for failing to hold Wall Street banks, executives, and other parties accountable for the excesses that resulted in the housing crisis. But other critics accused the Justice Department of a "shakedown" in how it reached the settlement with JPMorgan.
The Justice Department in November negotiated a wide-ranging deal with the largest U.S. bank that included a $2 billion civil penalty to resolve Justice Department claims.
It also included a $4 billion consumer relief package, and a separately negotiated $4 billion settlement with the regulator of mortgage financiers Fannie Mae and Freddie Mac.
Another $1.4 billion of the $13 billion package resolved a lawsuit from the National Credit Union Administration.
The settlement was released to the public, but not filed in federal court.
While the Justice Department enters into non-prosecution agreements on the criminal side without filing them in court, it rarely enters into similar out-of-court settlements over civil violations. The agency also did not release a complaint that it had prepared to file against JPMorgan before it negotiated the deal.
In its complaint, Better Markets alleges the settlement with the bank lacks critical facts that can help justify the deal, such as failing to name any individuals responsible for the wrongdoing, how much damage investors suffered or even "which specific laws were violated."
"No one has any ability to determine if the $13 billion agreement is fair, adequate, reasonable, and in the public interest or if this is a sweetheart deal entered into behind closed doors," the complaint says.
Kelleher, a former attorney at Skadden, Arps, Slate, Meagher & Flom, has become well-known for his critique of both Wall Street banks and regulators who he has often accused of failing to hold the banks accountable for wrongdoing.
Kelleher unveiled the lawsuit during a press conference at the National Press Club on Monday, armed with large posters including one with photos of Holder and JPMorgan Chief Executive Officer Jamie Dimon.
(Reporting by Sarah N. Lynch and Aruna Viswanatha; Editing by Karey Van Hall and Chris Reese)
By Sarah N. Lynch and Aruna Viswanatha