Greens deputy leader Adam Bandt has a tough fight on his hands to secure a second victory in the seat on Melbourne.
But he says he is confident he has done all he can to secure the votes he needs.
Mr Bandt won the seat from Labor in 2010 after long-serving MP Lindsay Tanner retired from politics.
The inner-city electorate includes the Melbourne CBD, Docklands, Richmond, Collingwood, Fitzroy, North Melbourne and Flemington.
The Liberal Party has chosen to preference against Mr Bandt in this election.
Mr Bandt won the seat on preferences in 2010, ahead of Labor's Cath Bowtell, who is running again this year.
, a reversal of its position in 2010.
A total of seven candidates are contesting the seat this year.
Mr Bandt is the only Greens member in the House of Representatives.
Speaking to the ABC at the Kensington Primary School polling booth, he said it will be close as he attempts to do what no other politician has been able to do.
"That is to elect a lower house MP despite Labor and Liberal working together on preferences," he said.
"I'm getting a lot of people who are telling me that they're disappointed in what Labor has been doing, especially with refugees and that they don't want Tony Abbott either and that they're switching their vote to us.
"I spoke to someone in North Fitzroy a couple of weeks ago who said 'I've been voting Labor for 20 years, it's just got to the point where I can't reward bad behaviour any more so I'm switching to you'.
"So we're certainly on track to increase our vote and if enough people in Melbourne vote Greens today for the first time we'll make history again."
Earlier, the ABC spoke to three young voters from the Melbourne Rowing Club: Jess Reifschneider, Brendan Shaw and Tess Lynch.
Ms Lynch says job security is a key issue for her, while the environment and infrastructure were important to Ms Reifschneider.
Ms Reifschneider described herself as a swinging voter and had not been very impressed with this year's election campaign.
Mr Shaw said young voters were disappointed with the drama of the past three years of parliament and were looking for real policies.
He felt this campaign had been too presidential and that many young voters had switched off.
Latest Politics Articles