The election is seen as a litmus test for the West African nation’s democratic transition.
Some 960,000 voters, almost half of the country’s population, are eligible to cast ballots.
Unemployment, economic recovery from the impact of the Covid pandemic, and whether Mr Jammeh should return from exile have been the central issues in the campaign.
Long queues have formed outside several polling stations, but many voters are not wearing masks or observing social distancing measures, the BBC’s Thomas Naadi in the capital, Banjul, reports.
The Gambia’s unique marble voting system – introduced in 1965 because of the country’s high illiteracy rate – is still being used.
On arrival at a polling station, and after their ID has been verified, a voter will be directed to a series of drums painted in the party colours of the different candidates.
Protruding from the top of each drum is a pipe into which the voter will slot a marble handed over by an election official.
Mr Jammeh fled into exile in Equatorial Guinea following his shock defeat in 2017. Last week President Barrow received a long-delayed government report on alleged abuses under his 22-year rule.
Hundreds of witnesses told the truth commission of state-backed executions squads and other rights violations including Aids patients being forced to take bogus cures.
Mr Barrow has promised to ensure justice for the victims.
The truth commission’s report sets the scene for a showdown between the two men, who have already abandoned a controversial pre-election deal their parties announced in September.
Six candidates in the running:
Adama Barrow (National People’s Party) – the incumbent
Ousainou Darboe (United Democratic Party) – a lawyer who briefly served as Mr Barrow’s vice-president. He was part of the coalition that brought down Mr Jammeh and is contesting for a fifth time
Essa Mbye Faal (Independent) – a lawyer and former lead counsel at the recently concluded TRRC. Contesting for the first time
Mama Kandeh (Gambia Democratic Congress) – came third in the 2016 contest, backed by Mr Jammeh
Abdoulie Ebrima Jammeh (National Unity Party) – a former teacher who once headed the country’s civil aviation authority. Contesting for the first time
Halifa Sallah (People’s Democratic Organisation for Independence and Socialism) – an MP contesting for the fifth time
