Correspondents say it's almost certain to be passed, since the coalition government commands a large majority.
But Antonis Samaras, the leader of one coalition party, New Democracy, has opposed a plan to commit to the latest bailout package in writing.
This puts him at odds with the new interim PM, Lucas Papademos.
But Mr Samaras said he would back the unity government in the vote.
However, the leader of Greece's Far Right Laos party, George Karatzaferis, said he would give unconditional support to Mr Papademos.
Mr Karatzaferis said he saw no reason to hold elections in February, as demanded by the New Democracy Party.
'Government of substance'
Mr Papademos has said his priority is ratifying the international 130bn euro ($177bn; £111bn) bailout package agreed at an EU summit last month.
It imposes austerity measures that have triggered widespread protest in Greece.
The crisis led to the resignation last week of the then-Prime Minister George Papandreou.
Mr Papademos, an unelected former banker, leads an interim cabinet of technocrats backed by the leading parties - including Mr Papandreou's Socialists (Pasok) and the rival centre-right New Democracy.
He said Greece needed to take bolder steps to tackle the crisis.
"Dealing with Greece's problems will be more difficult if Greece is not a member of the eurozone," Mr Papademos told parliament before the vote on Wednesday.
The leader of the conservative New Democracy, Antonis Samaras, has repeated that he will not heed an EU demand to sign a pledge to honour the latest bailout package, which will involve more austerity measures.
Mr Samaras, who faces opposition to the austerity measures from his own MPs, said that voting in favour of the government in Wednesday's confidence motion would suffice.
But the leader of the far right Laos party, George Karatzaferis, gave full backing to the new Prime Minister.
"I believe Papademos is best suited to cure all the ills of the Greek economy. In short, I trust him," he told Reuters in an interview, his first to foreign media since the formation of the new Greek cabinet.
"If we all keep interfering, it won't be a government of substance but a government for show," he added.
Mr Karatzaferis was a fervent backer of Mr Papademos for prime minister and stormed out of the presidential palace in anger last week when his candidacy was in doubt.
Power cut
On Wednesday, utility workers in Greece cut the electricity supply to the health ministry building in Athens.
They say the government has fallen 141m euros ($191m) behind on its bills to the public electricity company.
The workers are also protesting at being asked to collect an unpopular new property tax through household bills - people who don't pay the tax face the prospect of having their power supply cut.
Our correspondent says it's a sign of the social unrest that is still bubbling in Greece - and the resistance the new government is likely to face in the months ahead as it pushes through cost-cutting measures to save it from bankruptcy.
The unity government is intended to run the country until elections in February.
Greece must approve the latest bailout and implement policies linked to it, to secure a 8bn-euro ($11bn; £6.8bn) instalment from the first bailout.
Without the cash, Athens may have to default on its massive public debt.
The new package includes provisions for private holders of Greek bonds to write off 50% of their debt holdings.
Mr Papademos was named as interim prime minister last Thursday after days of turmoil sparked by Mr Papandreou's plan for a referendum on the bailout. That idea was later dropped.
