Zelensky's newly-created party is expected to win the largest share of the votes in the early polls expected to usher in a new era in the country dominated up to now by politicians who grew up in the Soviet Union.
The leader's party Servant of the People -- named after a sitcom in which he played a president -- is predicted to get roughly half of the vote even though it barely existed before Zelensky won a landslide victory in an April presidential vote.
Zelensky, however, may not secure a majority and would need to form a coalition, possibly with rock star Svyatoslav Vakarchuk's newly-created party Golos (Voice).
After casting his ballot, the 41-year-old leader said he would make a decision about possible coalition partners after the results of the vote are out.
"We do not see a coalition with the old authorities," Zelensky said in the capital Kiev, wearing a casual blue shirt.
The outgoing parliament, dominated by Zelensky's predecessor Petro Poroshenko, has been hostile to the actor, who called a snap election during his swearing-in as president.
The Ukrainian president must share power with parliament, which will nominate a prime minister and form a government.
Many said they voted for the leader's party.
"He was elected but he can't do anything. They (lawmakers) constantly put sticks in his wheels and dump his ideas," Valentyna, an 82-year-old pensioner told AFP in central Kiev.
Roman Andreykiv, 58, cast his vote for Zelensky's party because he wants the president and parliament to work in unison.
"Only then can they improve our lives," he said in the Western city of Lviv near the Polish border.
The rise of Zelensky and his party has been viewed as a rejection of Ukraine's political elite for failing to improve living standards, root out corruption and end the conflict with Russian-backed separatists that began in 2014 after a popular uprising ousted a pro-Moscow president.
Some said they wanted the former comedian and the rock singer to join forces to push through much-needed reform.
"I believe we have to make way for the young," 65-year-old Valentyna Moroz, who voted for the singer's party, said in Lviv. "I don't trust old politicians."
Oleksandr Zaporozhets, a 52-year-old builder from Kiev, said he also voted for Golos hoping the two anti-establishment politicians can help change the country of 45 million people.
"I hope together they can try and do something," he said.
Vakarchuk's Golos, which was established in May, is likely to make it to parliament, with polls showing support of between four and seven per cent.
Like Zelensky, Vakarchuk has packed his party with young people new to politics and banned any candidates who previously served as MPs from his list.
Speaking to reporters on Sunday, the rock star complained of low turnout and implored Ukrainians to vote.
"This is important because the country's future depends on you," he said.
There were relatively few voters at polling stations in Kiev on Sunday morning, in contrast to the second round of the presidential election in April, AFP reporters saw.
Of more than 20 parties fielding candidates, several others are predicted to win seats.
In a boon for the Kremlin, a pro-Moscow party called Opposition Platform-For Life is the second most popular in opinion polls, with up to 13 percent of voter support.
One of the party's top candidates, Viktor Medvedchuk is close to Russian President Vladimir Putin and claims he is his daughter's godfather. The two met for talks in Russia just days before the vote.
Poroshenko's party -- now renamed European Solidarity -- and the party of former prime minister Yulia Tymoshenko have up to eight and nine percent respectively.
No major instances of violence were reported on election day apart from a mine blast that killed two soldiers in eastern Ukraine.
A total of 225 of parliament's 424 members are elected through party lists, while the rest are selected directly in single-member districts.
Polling stations will close at 1700 GMT, with exit polls expected immediately afterwards.