Police have clashed with opposition supporters, some of whom have been blocking access to polling stations.
President Uhuru Kenyatta was declared the winner in an August vote, but it is being held again over “irregularities”.
The BBC’s Alastair Leithead in Nairobi says turnout so far appears to be much lower than the first time around.
Mr Kenyatta is seeking a second term. Opposition leader Raila Odinga has pulled out of the contest.
The polls on Thursday opened at 06:00 (03:00 GMT) with tens of thousands of police and other security staff deployed to protect voters and polling stations.
International observers have scaled down their missions for security reasons.
Unconfirmed reports say police have fired live rounds into the air to disperse opposition supporters in the western city of Kisumu and the Kibera area of Nairobi. Tear gas has also been used.
A voting official in Kisumu – opposition leader Raila Odinga’s home town – told the BBC just two of 400 polling station officials had turned up there, fearing they could face intimidation for taking part in the election.
One voter in Nairobi’s Mathare slum, taxi driver David Njeru, 26, told the AFP news agency: “It is my duty to vote. Last time the queue was all around the block and I waited six hours to vote, this time the people are few.”
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After casting his vote in the town of Gatundu, Mr Kenyatta urged people to cast their ballots so the country could move on.
“We’re tired as a country of electioneering. It’s time we moved forward,” he said.
He said most of Kenya was “calm and peaceful”
Voting under armed guard
Here at Moi primary school a small queue of people is lining up to vote under strict security. Armed police are on guard although this is an area some distance from any opposition strongholds.
But in opposition strongholds like Kisumu there are reports of empty polling stations and election officials too fearful to turn up for work. Some teargas has been fired at demonstrators in the Nairobi settlement of Kibera.
Western diplomats have called for calm and negotiations and condemned what they said were efforts to undermine the election commission and the judiciary. Though they don’t say it outright, the US and UK ambassadors and others don’t appear to have great confidence in this current electoral process.