The national vote on Jan. 25 will be closely watched by financial markets, nervous that a Syriza victory might trigger a standoff with Greece's European Union and IMF lenders and unleash a new financial crisis.
Read MoreGreece in 'critical' situation as Syriza leads polls
The survey, conducted on Jan. 13-15, showed that Syriza, which is running on a pledge to end austerity policies and renegotiate the country's debt, would win 31.2 percent of the vote if the election was held now, versus 28.1 percent for Prime Minister Antonis Samaras' New Democracy conservatives.
The centrist party To Potami (River) ranked third with 5.4 percent.
The leading party must generally receive between 36 and 40 percent of the vote to win outright, though the exact threshold depends on the share of the vote taken by parties that fail to reach a 3 percent threshold to enter parliament.
The electoral system automatically gives the winning party an extra 50 seats to make it easier to form a government.