The Taliban had threatened to attack polling places, but there were few incidents of violence reported.
Regardless, voters said they were undeterred by possible violence.
"See, wonderful people are coming to practice democracy," said Afghan lawmaker Shukria Barakzai. "We are not afraid of the threats. As much as they kill us, we get more stronger. As much as they killed our children, our journalists and innocent women, we say no, we will go and vote because we are fed up. We want to see real change, we want to enjoy our democracy."
"Today, I came to here to select my next president and I hope that whoever it is... is a good person, who will help the people and bring changes to Afghanistan," one voter said.
The newly elected president will replace current President Hamid Karzai, who has been constitutionally barred from leading the country again.
Results from the election are expected to start coming in Sunday.