Vucic is running for a second five-year term on a promise of peace and stability just as Russia has invaded Ukraine, which has put Serbia under pressure from the West to choose between its traditional ties with Moscow and aspirations to join the European Union (EU).
Polling group CRTA said turnout by 7pm local time, an hour before polling stations closed, was 54.6 per cent of Serbia's estimated 6.5 million electorate, compared with 44.9 per cent in 2020.
First preliminary results were expected within hours. Exit polls are not allowed by law.
CESiD and CRTA pollsters reported several irregularities, including photographing of ballots.
N1 TV station reported that an opposition leader, Pavle Grbovic, had been attacked and slightly injured not far from his polling station in Belgrade and showed footage of the incident filmed by a mobile phone. Grbovic confirmed the incident on Twitter.
Polls suggested Vucic, a conservative, was on course to win outright in the first round, ahead of Zdravko Ponos, a retired army general representing the pro-European and centrist Alliance for Victory coalition.
The opposition largely boycotted a parliamentary election in 2020, allowing Vucic's SNS party and its allies to secure 188 seats in the 250-seat parliament.
"Of course we do expect a huge victory, that's what we worked for the last four or five years," Vucic told reporters after voting.
Voters from Kosovo, Serbia's predominantly ethnic Albanian former province which declared independence in 2008, were taken to polling stations in Serbia proper by bus.
Russia's February 24 invasion of Ukraine has had a big impact on campaigning in Serbia, which is still recovering from the Balkan wars and isolation of the 1990s.
Serbia is almost entirely dependent on Russian gas, while its army maintains ties with Russia's military.
The Kremlin also supports Belgrade's opposition to the independence of Kosovo.
Although Serbia backed two United Nations resolutions condemning Russia's invasion of Ukraine, it refused to impose sanctions against Moscow.
Bojan Klacar, head of the CeSiD pollster, said the war had forced the focus of campaigning away from topics such as corruption, the environment and the rule of law.
A veteran politician who served as information minister in 1998 under former strongman Slobodan Milosevic, Vucic has transformed himself from a nationalist firebrand to a proponent of EU membership, but also of military neutrality and ties with Russia and China.
Ponos has accused Vucic of using the war in Ukraine in his campaign to capitalise on people's fears.
Opposition and rights watchdogs also accuse Vucic and his allies of an autocratic style of rule, corruption, nepotism, controlling the media, attacks on political opponents and ties with organised crime. Vucic and his allies have repeatedly denied all those allegations.
