They argue that there should be greater public acceptance of same-sex relationships.
Some 133 Tory MPs voted against plans to allow same sex marriage earlier.
Fifteen Labour MPs, four Lib Dems, eight Democratic Unionist and an independent were also against the move.
The rainbow flag was designed by Gilbert Baker in 1978 as a symbol of gay and lesbian community pride.
It first flew from government buildings during Pride 2012.
Deputy Prime Minister Nick Clegg said: "Flying the rainbow flag is a great symbol of pride - and what better place than Whitehall, the centre of government, to demonstrate that.
"I was proud to raise the flag for the first time last year, and hope to see more departments following suit this year."
Pride week, which will run from the 23-30 June, will this year have a theme of "love (and marriage)", in recognition of the equal marriage law which the government is pushing through Parliament.
Several Conservative MPs spoke out against the equal marriage law, but it passed the Commons with the help of Labour and Lib Dem votes.
Francis Maude has previously written that his brother, who was gay and died from AIDS in 1993, would have experienced a much better life if "there been greater acceptance of publicly acknowledged stable same-sex relationships".
A Cabinet Office spokesman said: "We are proud to fly the flag and look forward to a time when same sex couples can get married."
Francis Maude and Nick Clegg have agreed to demonstrate the government's commitment to equality by allowing the rainbow flag to fly from the Cabinet Office during Pride week.