Firebrand Prime Minister Orban has clashed repeatedly with other European Union leaders during his last term, especially with regard to the bloc's response to the refugee influx across Europe in 2015 and 2016.
Polls predicted his populist, right-wing Fidesz party would win a majority in the 199-seat legislature.
"Only a dramatic outcome of the election would force a significant shift in the direction of policymaking", Barclays said in a note. "Alongside high voter turnout, the country will have a strong, legitimate parliament". In 2014, the participation rate at the end of the day was 61.24 percent.
A man in the capital, Budapest, said he hopes the ruling party will win.
Polls officially closed at 7 p.m., but anyone waiting in line at that time has the right to vote and could therefore still cast their ballot.
"Today will decide whether Hungary becomes an emigrant country or not - and I wouldn't like Hungary to be an emigrant country", Mr Vona said.
The anti-immigrant campaign has gone down well with numerous roughly two million core voters of Fidesz.
"Voter turnout is at record high", tweeted Tamas Boros, co-director of the Policy Solutions think tank.
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Figures from Hungary's National Election Office show that voters are turning out in very high numbers for the country's parliamentary election.
There is also a slight chance that the fragmented opposition could strip Fidesz of its parliament majority if voters frustrated with Orban's policies choose tactical voting in the 106 constituencies.
"From here I will go and take part in mobilizing voters". However, local media broadcast images of voters still queuing up to cast their ballots at a number of polling stations. The opposition Socialist Party urged authorities to "at least distribute water" in districts where voters were waiting in line, sometimes for hours.
Clad in a green jacket and white shirt, Jobbik leader Gabor Vona, 39, arrived to vote in the eastern city of Gyongyos, his home town and the district where he is likely to win a seat.
Vona said: "I feel a surprise and a Jobbik breakthrough can be expected in the election". In Hodmezovasarhely, a Fidesz stronghold in southeastern Hungary, voters complaining of graft, cronyism, and intimidation elected an independent in a February mayoral election for the first time in two decades.
Karacsony, who heads the joint list of the Socialist Party and the Dialogue party, also said President Janos Ader, a former lawmaker for Orban's Fidesz party, had "omitted a very serious task" by not calling for Hungarians to cast their ballots in the election.
Orban himself voted early on Sunday morning with his wife at a school in the leafy Zugliget suburb of Budapest.
Orban's election campaign focused on his staunch anti-migration policies despite opinion polls suggesting that many Hungarians are actually more anxious about other social concerns such as poverty, corruption and improving funding for the country's ailing health care system.