The opposition says Vucic is trying to concentrate power in his own hands in the small Balkans country of 7.1 million where the average salary is one of Europe's lowest.
The post of president has largely been ceremonial in recent times but analysts believe that it would be a much more influential position if occupied by Vucic.
Vucic is hoping to clinch the election in the first round by winning more than 50 percent of the vote. If he fails, there will be a second round of voting in a fortnight.
Ultranationalist Vojislav Seselj, one of 11 candidates running in the election, has argued that "all the power should not be concentrated in the hands of a single man, Aleksandar Vucic."
EU or Russia?
Vucic's centre-right Serbian Progressive Party is pro-EU and in favour of the country's accession.
But the majority of the population is made up of Orthodox Slavs with little fondness of the European Union and a closer affinity to traditional ally Russia.
Fully aware of this balancing act, Vucic travelled to Moscow just a week before the vote to discuss the delivery of six Mig-29 aircraft.
Vucic has run a typically bullish campaign, with a video showing a plane marked "Serbia 2017" about to crash for a lack ofleadership and taking out full-page ads in the press.
He has accused opponents of receiving "millions of euros (from) certain foreign countries", without specifying.
Vucic has touted economic success since becoming prime minister in 2014, achieving growth of 2.8 percent last year and cleaning up the public finances.
But the average Serbian earns a mere 330 euros ($355) per month while unemployment is running above 15 percent.
'Dangerous' second round
The opposition hopes to force Vucic into a second round, which could be "dangerous" for the prime minister, according to political analyst Dusan Janjic.
Polls show his main challengers are former ombudsman Sasa Jankovic and ex-foreign minister and Vuk Jeremic, who ran an unsuccessful campaign to be UN chief.
They are expected to get up to 10 percent each, followed by Seselj, who was acquitted last year of war crimes during the bloody breakup of the former Yugloslavia.
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.
Using the fictional name of Ljubisa Preletacevic -- nicknamed "Beli" (White) -- he could even come second in the race behind Vucic, some analysts say.
One political expert, Jadranka Jelincic, has warned however that the election was "a way of diverting attention from serious issues."
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