Reports says Mr Duterte led polls ahead of voting, despite controversial comments while campaigning and a hard-line stance.
It was noted that the campaign was driven by fears about the economy, inequality and corruption.
Voting was extended for an hour in some areas after glitches with vote-counting machines.
More than 100,000 police officers were on duty amid violence ahead of the election.
Seven people were shot dead in an ambush by unknown gunmen in the town of Rosario, in Cavite province, south of the capital, Manila.
According to the report the region had been considered an area of concern because of its political rivalries.
On Saturday, a mayoral candidate was murdered in the south of the country.
President Benigno “Noynoy” Aquino is standing down as the constitution limits presidents to one six-year term.
Filipinos would also pick a vice-president and local officials.
The election campaign has focused on reforming the economy, infrastructure, tackling corruption and crime and on the territorial disputes with China in the South China Sea.
It was said that Elections were peaceful, communal affair with large family groups or neighbours walking into the polling stations to vote together.
The constant crowds coming in and out of the elementary school in Manila’s Tondo district looked hard to manage.
But Election officials were said to be well-practised, and voters well-informed.
Plenty of officials were available to help voters manage the formidable ballot sheets, listing in this constituency dozens of candidates for the various local and national posts.
The enthusiasm across the age and class spectrum for Mr Duterte in this campaign had exposed the weariness of Filipinos with the familiar political faces, who have delivered some economic improvements.
Mr Duterte has suggested that “he would disregard democratic checks and balances if they get in the way of fixing the country’s problems”.
It’s a message that had excited and attracted people. Yet the numbers coming to vote here, and the positive and relaxed atmosphere, show that the faith in the familiar rituals of democracy was still as strong as anywhere in Asia.