The polling stations opened at 7:00 am (0400 GMT) on Saturday and close at 5:00 pm (1400 GMT), with preliminary results due in the coming days.
About 2.8 million Kurds are eligible to vote across the three-province region of northern Iraq.
The campaign centered on calls for more to be done to fight corruption and improve the delivery of basic services, as well as on how the energy-rich region's oil revenues should be spent.
The election, the first since July 2009, sees three main parties jostling for position in the 111-seat Kurdish parliament.
The Kurdistan Democratic Party (KDP) of regional president Massud Barzani is widely expected to win the largest number of seats, although it is unlikely to obtain a majority on its own.
The Patriotic Union of Kurdistan (PUK), which is in government with the KDP, however faces a challenge from the Goran movement in its Sulaimaniyah province stronghold.
The challenge has been heightened by leadership questions as the party's veteran leader, Iraqi President Jalal Talabani, recuperates in Germany from a stroke.
Internationally, the focus is likely to be on the region's drive for greater economic independence from the federal government, with which it is locked in multiple disputes.
Iraqi Kurdistan enjoys a high level of autonomy from Baghdad, and the regional parliament has passed laws on a wide range of issues.
Kurdistan also operates its own security forces and visa regime and has control over an array of other responsibilities.
RA/HH