"On my way to the United States to strengthen resilience and defence capabilities of Ukraine," Zelenskiy said on his Twitter account early on Wednesday.
Russia calls its invasion in Ukraine a "special military operation" to denazify and demilitarise its neighbour.
His wife, Olena Zelenska, travelled to Washington in July to address Congress and has made several other international trips pleading for Ukraine, as have his aides and ministers.
In contrast, his Russian counterpart, President Vladimir Putin, has spent much of his time inside the halls of the Kremlin.
Reporting in Kyiv by Pavel Polityuk; Writing in Melbourne by Lidia Kelly Editing by Shri Navaratnam, Robert BirselOur Standards: The Thomson Reuters Trust Principles.