April 5 (Reuters) - Proxy advisor CGI Glass Lewis has asked shareholders of Australia's Woodside Energy to vote against the re-election of Chairman Richard Goyder and against the company's climate strategy at the annual general meeting later this month.

Glass Lewis noted that activist investor Australasian Centre for Corporate Responsibility (ACCR) opposed Goyder's re-election, with ACCR saying last month that Woodside's board was persistently unresponsive to shareholder concerns on climate risk management.

Goyder, who is also the chairman on Qantas Airways, will step down from the airline's board in late 2024, with the Australian flag carrier looking to fix its battered reputation after being beset with both legal and regulatory actions.

"Considering Goyder's role as chair of Qantas, some shareholders may find his accountability for oversight failings relevant in assessing his suitability as the chair of Woodside," Glass Lewis said in its report.

Glass Lewis' recommendation comes after HESTA, one of Australia's largest pension funds, urged Woodside last month to consider appointing new directors who are equipped to manage climate-related challenges.

Last year, nearly 49% of investor votes were against the company's climate plan, which Woodside put to an advisory vote for the first time.

Woodside is set to hold its annual shareholders meet on April 24.

"The Woodside board believes Goyder is a highly capable and effective leader," a Woodside spokesperson said on Friday. (Reporting by Himanshi Akhand and Roushni Nair in Bengaluru; Editing by Shounak Dasgupta)