Mugabe will step down if he loses today's elections
Campaigning was mostly peaceful, with few reports of intimidation.
Zimbabweans are voting in fiercely contested presidential and parliamentary elections which have already been hit by fraud allegations.
President Robert Mugabe, 89, has said he will step down after 33 years in power if he and his party lose.
Prime Minister Morgan Tsvangirai's Movement for Democratic Change (MDC) have accused Mugabe's party of doctoring the electoral roll, a charge it has denied.
Campaigning was mostly peaceful, with few reports of intimidation.
The government has barred Western observers from monitoring Wednesday's elections, but the African Union (AU) and the Southern African Development Community (Sadc), as well as local organisations, have been accredited.
The turnout is expected to be high among the 6.4 million people registered to vote, with tens of thousands of people attending rallies in recent weeks. Results are expected within five days.
Wednesday has been declared a national holiday to ensure people can vote.
To be declared a winner, a presidential candidate must win more than 50% of the vote. If no candidate reaches this mark, a run-off will be held on 11 September.
The elections will be the first to be held under the new constitution approved in a referendum in March this year.