More than 70,000 security forces have been deployed across the country to counter Taliban militants who have vowed to target polling stations.
The twice-delayed vote is taking place after Taliban-US peace talks collapsed earlier this month.
The two main candidates are the incumbent, Ashraf Ghani, and chief executive, Abdullah Abdullah.
Shortly after voting began, there was an explosion near a polling station in the southern city of Kandahar, which injured at least 16 people.
Independent Election Commission spokesman Zabi Sadaat told the AFP news agency: “Voting has begun all over the country, and we are glad the people are already in big lines at polling centres waiting to cast their votes.”
Turnout is expected to be low but one voter said she would cast her vote even if it meant standing in long queues for hours.
“Bravado gets defined when one musters courage to cast their vote in Afghanistan,” said Roya Jahangir, a doctor based in the capital, Kabul.
“We hope this time there is no fraud – otherwise voters will feel cheated once again,” she told Reuters news agency.(BBC)
Why does this election matter?
Afghanistan’s next president will lead a country devastated by four decades of war.
The conflict continues to kill thousands of people every year, drawing in forces from around the world.
Nearly two decades since the international community intervened, the US has been trying to negotiate an end to the conflict with the Taliban. The US currently has about 14,000 troops in Afghanistan, and there are thousands more from countries like the UK, Germany and Italy, there as part of a Nato mission to train, advise and assist the country’s security forces.
Whoever is elected president in the fourth election since US-led troops ousted the Taliban in 2001 should have a key role to play at a crucial moment in the country’s history.