Voting has in general been peaceful and smooth in Kenya despite some delays and problems with the electronic kit in some parts of the country.
This vote follows an intense campaign dominated by debates about living costs, unemployment and corruption.
The frontrunners for president were ex-Prime Minister, Raila Odinga, and current Deputy President, William Ruto.
The outgoing President, Uhuru Kenyatta,was backing his former foe, Mr Odinga, after a fall out with Mr Ruto.
Just over 30 per cent of the 22 million registered voters had cast their vote by noon local time (09:00 GMT), the Electoral Commission has said.
MrOdinga was mobbed by supporters when he went to vote in Kibra – one of his strongholds in the capital, Nairobi.
He did not speak to the press, but his wife, Ida Odinga, said he was “upbeat about the election”.
When Mr Ruto voted in the town of Eldoret in the Rift Valley, he pledged to accept the election result.
“I think for the first time in the history of multi-party democracy in Kenya, all the candidates have undertaken that they will accept the outcome of the results,” he told the BBC.
A dispute over election results in 2007 led to weeks of violence leading to the deaths of an estimated 1,200 people, and forced about 600,000 people to flee from their homes. -BBC