By Agence France-Presse
A Nine-Galaxy poll showed Labor beating the governing Liberal coalition 52-48, which would signal a clear parliamentary majority.
It would see former union leader Bill Shorten become prime minister after six years of conservative government.
The poll canvased 3,300 voters in 33 seats and echo pre-vote surveys that tipped Labor to win.
The poll was released shortly before the first voting stations closed in the east of the country at 6:00 pm (0800 GMT), with voting to continue for another two hours in the west of the country.