Prime Minister Kevin Rudd has been asked to allow Labor MPs a free parliamentary vote on gay marriage.

Australian Greens senator Sarah Hanson-Young is hoping her bill to allow marriage regardless of sex, sexuality and gender will be debated by parliament in the new year.

"I'm calling for the prime minister to ... grant his members a conscience vote so we can get a true reflection of how the Australian community is feeling," she told ABC Television on Monday.

Removing discrimination from the Marriage Act would bring Australia into line with Canada, Spain, Belgium and some parts of the United States, she said.

A Senate committee, sitting in Melbourne on Monday, will hear evidence from gay marriage advocates, family groups, the Catholic Church and the Australian Christian Lobby.

The committee has received nearly 10,000 submissions on the bill, Senator Hanson-Young said.