Volodymyr Zelensky became president in a landslide victory in April but says he has so far been unable to appoint the ministers he wants.
The ex-TV star hopes this snap election, which he called after being sworn in, will consolidate his power and give a greater mandate for reform.
Mr Zelensky's Servant of the People party, named after the TV show he starred in, is expected to win the poll.
Asked by the BBC's Steve Rosenberg outside a polling station in Kiev just how important the election was, Mr Zelensky told him: "Maybe more important than the presidential election."
Polls suggest the second most popular party is the pro-Russian Opposition Platform - For Life, and that it is set to pick up votes in the east.
However, Mr Zelensky has ruled out working with it should he need to form a coalition.
Instead he would rather partner with Holos (The Voice) - another new party led by rock star Svyatoslav Vakarchuk.
The president needs to share power with the Verkhovna Rada, Ukraine's parliament, which will form a government and nominate a prime minister.
Mr Zelensky told our correspondent that the "president, prime minister and parliament have to work together, just to make life happy for Ukraine".
He said the key issues were investment, democracy and safety.
Polling stations across Ukraine will close at 20:00 local time (17:00 GMT).
The comedian president
Mr Zelensky was known for his comic role on TV as a teacher who wins the heart of the nation and becomes president after his expletive-laden rant about politics goes viral.
In reality, his route to the leadership was a bit more conventional than in his show - but only a bit.
After shunning official rallies and speeches, demanding his opponent take a drug test and openly admitting he didn't have any strong political views, he scored a landslide victory in April and unseated the former political heavyweight, Petro Poroshenko.
Now Mr Zelensky hopes to make waves again this weekend by sweeping aside the old guard and bringing in fresh blood.
One of the candidates for Servant of the People, for example, is Zhan Beleniuk, an Olympic wrestler who wants to become Ukraine's first mixed-race MP.
Mr Poroshenko, meanwhile, is still hoping for victory this weekend.
However, his party - rebranded European Solidarity to remove his name - is currently polling at about 8%, just over the 5% threshold needed to enter parliament.