TONY Abbott's lesbian sister says she isn't going to try to convince her brother to change his mind on gay marriage.

Christine Forster, who is running for a place on the City of Sydney Council, has described herself as "a small-l liberal and a big-L lesbian'' and is in a committed same-sex relationship.

"I'm absolutely 100 per cent in support of marriage equality,'' Ms Forster told reporters in Sydney today.

"My brother holds a different view. He believes in the terms of the marriage act as they exist at the moment.

"He is entitled to have his opinion and he's a man of great conviction.

"He and I have a difference - that's what happens in families and that's where it stays.''

Ms Forster is on the Liberal Party ticket for September's council elections alongside computer entrepreneur Edward Mandla, who is seeking to topple Sydney Lord Mayor Clover Moore.

The Liberal team today unveiled the centrepiece of its plan for Sydney - a 10 per cent rate cut for the city's residents and businesses.

"Sydney is the seventh most expensive city in the world - 50 per cent more expensive than New York,'' Ms Forster said.

"Clover Moore has lost her way. We have a plan to cut the wasteful spending and overcharging.''