The draft law submitted by Ukrainian president Petro Poroshenko was supported by 282 lawmakers during a plenary session.
"We need to make an extremely important, extremely decisive step in the fight against corruption in our state," parliamentary speaker Andriy Parubiy told his colleagues ahead of the vote.
President Poroshenko said he was "satisfied" with the result.
"I call on MPs not to delay (the law's) adoption as a whole," he wrote on his Facebook page.
The new court is to investigate high-profile corruption cases and is seen as the missing link in a chain of institutions created after Ukraine started large-scale reforms.
In mid-February President Poroshenko urged MPs to find a compromise on the draft law, which in its current form has faced heavy criticism from the IMF.
The IMF said in January that "several provisions (of the bill) are not consistent with the commitments of the authorities", in a letter published by the Ukrainian media.
The IMF insists that the anti-corruption court should work in coordination with the newly founded National Anti-Corruption Bureau of Ukraine and the Specialised Anti-Corruption Prosecutor's Office, as well as focus "solely on corruption-related cases".
Ukraine was ranked 131st out of 176 countries in Transparency International's corruption perception index in 2016.
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