Liberal Democratic Party Senator David Leyonhjelm has announced his intention to introduce a private member's bill to legalise same-sex marriage.

Two years ago the House of Representatives voted down same-sex marriage laws.

However, Senator Leyonhjelm says on Tuesday he will publicly confirm plans to introduce similar legislation, and is hoping Coalition MPs will be granted a conscience vote on the issue.

"I've discussed this issue with a couple of Coalition senators and I don't think that's an insurmountable obstacle, but yes that is the situation at the moment," Senator Leyonhjelm said.

New South Wales independent MP Alex Greenwich was part of a cross-party group which failed to get acceptance for similar legislation in his state, and says Senator Leyonhjelm has a better chance.

"I hope that it dispels the myth that this is an issue of the left side of politics and I think having it come from a conservative senator will certainly help that cause," Mr Greenwich said.

"The senator will need to work with people across the parliament to ensure it progresses and I know he's committed to that."

Ivan Hinton from the Australian Marriage Equality group says circumstances have changed since the 2012 bill was voted down.

"We know that support for marriage equality is only getting stronger in the community," Mr Hinton said.

"We know that there has been an enormous number of couples get married in overseas jurisdictions and come home and have their marriages unrecognised.

"It's certainly time for the Federal Government to reflect these relationships that already exist."

Senator Leyonhjelm and other new crossbenchers have spent their first week in the Senate debating legislation to axe the carbon tax.