In a three-way race, incumbent Taiwan leader and ruling Kuomintang (KMT) chairman Ma Ying-jeou is competing for Taiwan's next leadership role with major opposition Democratic Progressive Party (DPP) chairwoman Tsai Ing-wen and the minority People First Party (PFP) chairman James Soong.
Ma, who is seeking a second four-year term, cast ballot in Taipei Saturday morning, while Tsai and Soong cast ballots in the New Taipei city nearby.
More than 14,000 polling stations opened across the island. Local election affairs authority estimated that about 80 percent of the island's 18 million eligible voters will turn up at polling stations.
At some polling sites at schools in Taipei and New Taipei, Xinhua reporters saw that the electorates, carrying identification cards, personal seals and letters of notice to vote, got ballot sheets from the polling sites, marked them at places fenced with cloth and then put them into ballot boxes.
The voting has proceeded smoothly as of 10:30 am.
The "legislative" elections is being held simultaneously in Taiwan, for the first time, in order to save costs.
For the "legislative" poll, 283 candidates are running for 79 directly elected regional and aboriginal seats, and 127 candidates from 11 parties are vying for 34 at-large seats. Taiwan's "legislature" has 113 seats.
Each eligible voter will cast two ballots in the "legislative" elections - one for a candidate representing the voter's district and the other for a political party to decide how many at-large seats each party can obtain, according to the island's election commission.