One poll by state television NET said the conservative New Democracy Party has won 45.5% of the vote, against 40.2% for the ruling socialist PASOK party. Another exit poll by private television network Antenna says New Democracy will score between 45.6% and 48% of the vote, with PASOK ranging between 38.8% and 41.2%.
The margin of error is 1.5%.
Under Greece's electoral system, the biggest party usually wins an absolute majority of seats in the country's 300-strong parliament, even if it beats the runner-up just by a handful of votes.
Greece's next government faces two major challenges: completing preparations for the Olympic Games which will be held in Athens in August and seeing through talks to reunify the divided island of Cyprus, in which Greece and arch-rival Turkey are involved.
The conservatives appeared confident, however, after maintaining a steady lead in opinion polls for months. Conservative leader, Costas Caramanlis, cast his ballot early.
“This is the day of the voters and we have absolute confidence in their judgment,” Mr Caramanlis said.
Four years ago, the Socialists managed a slim 1% victory. This time, they have turned to former foreign minister George Papandreou - the 51-year-old son of the party founder - as their leader in an attempt to ride his popularity to a fourth consecutive term.
There are fears a Conservative victory could lead to labour unrest from Greece's Socialist-dominated unions as Olympic deadlines near.