It is expected to be a tight race between President Edgar Lungu’s governing PF party and the opposition UPND led by Hakainde Hichilema.
For the first time, a presidential candidate must win more than 50% of the vote to avoid a run-off.
Mr Lungu won the last election by less than 28,000 votes.
Each of the nine presidential candidates has a running mate to avoid a presidential by-election if the president dies in office – which has happened twice in the last 10 years
The BBC’s Akwasi Sarpong in the capital, Lusaka, says there has been a high turnout so far at polling centres in the city.
Long, calm, orderly queues have formed and election monitors have not reported any complaints, he says.
Observers say Zambia’s struggling economy will be a key issue.
Plunging prices for copper, its main export, have closed mines and left thousands unemployed. With economic growth roughly halved, the country asked the International Monetary Fund for help earlier this year.
In addition, Zambia, like other parts of southern Africa, has been hit by a drought that the UN has described as the worst in 35 years.
The UPND (United Party for National Development) has accused President Lungu of presiding over the “collapse” of the economy. But the PF (Patriotic Front) says it has a plan to diversify the economy.
During the last election, some women wearing nail varnish were forced to remove it before voting as polling officials said they would not be able to apply the indelible ink correctly.
But on Wednesday night, the electoral commission circulated posts on social media saying women with “painted nails and/or false nails” could vote.