The call to clean-up government come as a survey found 85% of Australians believe some politicians are corrupt.
In a letter to prime minister Scott Morrison, 34 ex-judges, including Sir Gerard Brennan, the former chief justice of the High Court of Australia, say there is public suspicion that corruption is behind many government actions.
The letter says "secrecy is at the core of corrupt conduct", adding: "Existing federal integrity agencies lack the necessary jurisdiction, powers and know-how to investigate properly the impartiality and bona-fides of decisions made by, and conduct of, the federal government and public sector.
"A national integrity commission is urgently needed to fill the gaps in our integrity system and restore trust in our democracy."
The letter comes as an increasing number of Australians say they believe government corruption is rife.
Transparency International Australia, an anti-corruption organisation, carried out a survey in June that found 85% of people believe at least some members of the national parliament are corrupt, and two-thirds of Australians support the creation of a national anti-corruption body.
A minister in the state of New South Wales was jailed last year for wilful misconduct in public office, after awarding a mining licence without a competitive tender.
AJ Brown, professor of public policy at Griffith University and board member of Transparency International, said there have also been concerns over senior public servants winning lucrative consultancies or board positions from firms which then win contracts from their previous departments.
The judges' letter was coordinated by progressive think-tank The Australia Institute, which worked with legal experts to design an anti-corruption body.
Australia Institute researcher Hannah Aulby said their goal was to support transparency in the political process.
Independent MP Cathy McGowan plans to table a bill to establish a national anti-corruption body in the federal parliament.
The Labour opposition supports a national anti-corruption body but the ruling conservative minority government is against the move.
Attorney general Christian Porter said such a model would have extraordinary powers against public servants with a definition of "corruption" that was too broad.
He said: "Those powers could be used without proper checks and balances."