Syriza, led by 40-year-old Alexis Tsipras, leads the incumbent conservative New Democracy party of Prime Minister Antonis Samaras by around four points, according to pre-election opinion polls.
Some 9.8 million people are eligible to vote. Polling stations close at 1700 GMT, followed immediately by the results of exit polls.
Tsipras wants to renegotiate Greece's massive 318-billion-euro (USD 356 billion) debt and end the wage cuts and public spending reductions linked to its bailout by the European Union and International Monetary Fund.
Elli, a 20-year-old student casting her ballot in the middle-class Athens suburb of Nea Smyrni, said she would vote for Syriza, but admitted she had concerns.
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"I was undecided until this morning because I'm afraid that the outcome of a Syriza win could be a default," she told AFP. "We need to stay in Europe."
Yannis Papacostas, a 50-year-old self-employed man, said he wanted the Greek people to "wake up" after six years of economic hardship.
He said he would vote for To Potami (The River), a new party that could form part of a coalition government.
Tsipras has pledged to restore "dignity" to Greece and confront the so-called troika -- the EU, IMF and European Central Bank (ECB) -- which imposed the conditions linked to a 240-billion-euro bailout deal that began in 2010.
The Syriza leader says Greece has been put in an "unsustainable" position, forced to make spiralling debt repayments while the economy shrinks.
The IMF, meanwhile, has warned Greece that failure to repay its debts will carry "consequences".
"I want Greece, despite the difficulties, to remain part of our story," Merkel said Friday.
Greece has seen a rapid economic decline since the eurozone crisis began, pushing unemployment above 25 per cent.