Exit polls suggest that the opposition Georgian Dream coalition, led by billionaire Bidzina Ivanishvili, had a clear lead in votes for party lists.
But President Mikheil Saakashvili said his ruling party was winning in the race for the seats decided on a first-past-the-post basis.
Official results from Monday's vote are expected within hours.
In the election, 77 out of 150 parliamentary seats were contested in the proportional vote, while the other 73 seats were determined on the first-past-the post basis.
Thousands of cheering supporters of Georgian Dream gathered to celebrate in the capital Tbilisi after the polls closed late on Sunday.
"We have won! The Georgian people have won!" Mr Ivanishvili said in a speech broadcast on a Georgian TV station, the AFP news agency reports.
Mr Ivanishvili, Georgia's richest man, said he expected his coalition to win 100 out of 150 parliamentary seats.
In televised comments, Mr Saakashvili conceded the opposition "has won the majority in the proportional vote".
But he added that "in single-mandate constituencies, the majority of votes has been secured by Georgia's (ruling) United National Movement".
A spokeswoman for the United National Movement predicted that it have "a solid majority".
Mr Saakashvili had sought to portray the election as a choice between his Western-leaning government, and a future in which he said Mr Ivanishvili would allow Russia to dominate the former Soviet republic.
Georgia's Central Electoral Commission (CEC) said in a statement that turnout had been around 61% and added voting had taken place "in a peaceful and transparent manner, with no serious incidents reported".
Earlier Mr Ivanishvili had staged a symbolic protest by refusing to vote, saying the authorities had "already resorted to very many violations".
The poll is being seen as the biggest test of President Saakashvili's popularity since he came to power in 2003 in the so-called Rose Revolution.
The BBC's Damien McGuinness in Tbilisi says that if the ruling party gets back into power despite failing to secure a majority of votes, the opposition could feel cheated of victory - and spark mass protests.
The government's reputation has taken a battering in recent weeks because of a prisoner-abuse scandal.
Videos broadcast on national television showed prison inmates being beaten and sexually abused by guards.
The scandal sparked street protests and allowed Mr Ivanishvili to portray the government as high-handed.
Human rights group Amnesty International says many of Mr Ivanishvili's supporters were "fined, fired, harassed or detained for expressing their political views" during the election campaign.
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