Vucic, the 47-year-old prime minister, is hoping to clinch more than 50 percent of the ballot, winning a five-year mandate as president outright.
Most surveys tip Vucic for an easy victory in the face of a divided opposition. But if he fails to win a majority in the first round, a second round run-off will be held on April 16.
The post of president has largely been ceremonial in recent times but analysts believe it would be a much more influential position if occupied by Vucic.
But the average Serbian earns a mere 330 euros ($355) per month while unemployment is running above 15 percent.
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The opposition has been unable to field an united candidate to run against him, so Vucic faces a wide range of challengers.
There are 10 opposition candidates bidding for president, including former ombudsman Sasa Jankovic, ex-foreign minister Vuk Jeremic and ultranationalist Vojislav Seselj.
And shaking up the race is Luka Maksimovic.
He campaigns in a Borat-style white suit, sports a samurai-style ponytail and hipster beard, touts a manifesto studded with lunatic pledges and uses a made-up name that mocks politics as the circus of greed.
Opposition candidates have presented the vote as a referendum on Vucic, whom they accuse of trying to consolidate power for himself.
Ultranationalist Seselj argues that "all the power should not be concentrated in the hands of a single man, Aleksandar Vucic."
Some voters echoed this position.
"I cannot deny that Vucic works a lot, that he is a friend with both the West and Russia. But I do not want all the power to be in the hands of one politician any more," said 59-year old taxi driver Mihajlo.
The progress made by the Vucic government "is already not bad. It should continue faster in the same direction," she told AFP.
Both the opposition and independent media monitoring groups have cried foul over the omnipresence of Vucic in the media.