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.
According to the electoral commission, some 10.5 percent of some 6.7 million eligible voters cast their ballot in first three hours of vote.
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.
Vucic has touted economic success since becoming prime minister in 2014, achieving growth of 2.8 percent last year and cleaning up public finances.
But the average Serbian earns a mere 330 euros ($355) per month while unemployment is running above 15 percent.
"I am thrilled with the way things are going on right now," Dzehva Trikic, 76-year old pensioner, told AFP after casting her ballot.
"Serbia will bloom" with Vucic, she said.
But 26-year-old unemployed Vuk Rancic from the southern town of Nis said he voted hoping for a change.
"If something changes fine, if not, I'm going out of here," Rancic said.
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 stands out on the campaign trail, in an all-white suit, with samurai-style ponytail and trim beard.
His political style is as unusual as his fashion style, with a penchant for making outlandish pledges and using a made-up name -- Ljubisa Preletacevic, nicknamed "Beli" (White) -- that mocks politics as an arena of greed.
Beli could even come second in the race behind Vucic, some analysts say.
'I will respect constitution'
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."
But Vucic, who came to vote with his teenage daughter shortly after the polls open at 7 am (0500 GMT), rejected the opposition accusations as "ridiculous".
"They can say whatever they want. I will respect Serbia's constitution. That is my obligation and that is what I will do," the 47-year-old told reporters after casting his ballot in New Belgrade.
Both the opposition and independent media monitoring groups have cried foul over the omnipresence of Vucic in the media.
In the week leading up to the vote, national TV channels devoted 51 percent of their airtime to Vucic, more than all the other candidates put together, according to analysis by the Kliping research agency published in the Danas daily.
On Thursday, the last day of the campaign, all but two of the dozen or so national dailies appeared wrapped in full-page ads reading: "On April 2, give a decisive vote to Aleksandar Vucic."
Political analyst Boban Stojanovic said he "wonders if after such a campaign, the elections could be free and fair."
Second-round hopes
Ex-ombudsman Jankovic, seen as a key Vucic rival, has also claimed public sector workers have been intimidated ahead of the vote, citing testimony to that effect.
The opposition hopes to force Vucic into a second round, which could be "dangerous" for the prime minister, according to political analyst Dusan Janjic.
"After this (vote) nothing in Serbia will be the same any longer," Jankovic said after voting with his family in Belgrade. "We will begin to put things in order."
Vucic has run a typically aggressive campaign, with a video showing a plane marked "Serbia 2017" about to crash for a lack of leadership.
He has accused opponents of receiving "millions of euros (from) certain foreign countries", without offering specifying charges.
The opposition fears electoral fraud, in particularly in Albanian-dominated Kosovo where some 120,000 Serbs live.
Polls close at 8:00 pm. The first results are expected before midnight.
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