Page last updated at 12:19 GMT, Sunday, 27 June 2010 13:19 UK
The poll follows a pledge by military ruler Sekouba Konate to return the country to civilian rule. He has vowed not to stand or allow any members of his administration to do so.
Twenty-four candidates are vying for the presidency.
Guinea has been ruled by a succession of military and civilian autocrats since independence in 1958.
The army seized power in 2008, following the death of strongman Lansana Conte, who had been in power for more than two decades.
The country descended into chaos last September, after troops opened fire on pro-democracy demonstrations in the capital, Conakry, killing more than 150 people.
‘Judgment of history’As voting got under way on Sunday, Conakry resident Marieme Kande told AFP news agency: “I am happy to vote freely.”
The BBC’s Alhassan Sillah in the capital says there is real optimism that the vote could finally drive the army out of politics, leaving democratically chosen leaders to try to improve people’s lives.
Voters have cast ballots in large numbers across the country.
In neighbouring Liberia – where many Guineans fled violence in recent years – exiles have been voting in the capital Monrovia, with queues stretching five kilometres (three miles).
The frontrunners are former Prime Ministers Cellou Dalein Diallo and Sidya Toure, and veteran opposition leader Alpha Conde.
On Saturday, Gen Konate said that the country was standing “before the judgement of history.”
“Starting from now, it’s up to you to make it happen,” he told the candidates.
The choice, he added, was between “peace, freedom and democracy, or chaos and instability”.
Despite having rich reserves of bauxite, iron and diamonds, Guinea is one of the poorest countries in the world.
Election results are expected within three days. As no candidate is likely to win outright, a run-off between the front-runners is due to take place on 18 July.