Polling stations opened at 7am on Sunday (0500 GMT) and will close at 7pm, with results expected on Monday.
Rama, in power as head of the Socialist Party since 2013, is favourite to win against his old rival, former prime minister Sali Berisha of the Democratic Party, bolstered in part by an influential network built during 12 years in power, a recent period of healthy economic growth and a largely popular image abroad.
But opposition to Rama has intensified in the past year over a perceived crackdown on the opposition - and Berisha - while Rama weathered a series of scandals, including the arrest of his ally, the mayor of Tirana, Erion Veliaj, on allegations of corruption and money laundering.
Veliaj and Berisha deny wrongdoing.
Rama has spent the past week reiterating his promise to join the EU by the end of the decade, although some experts doubt that timeline will be possible given the reforms required to join the bloc, including eradicating graft.
"We will get our fourth mandate, and we will not lose a single day for Albania 2030 in the EU," he said at his final campaign rally on Friday.
Many young voters, especially, are tired of Berisha and Rama, who have run the country in various roles since the fall of communism in 1990.
They point to Albania's stark income inequality that sees many people drive expensive Range Rovers around the capital Tirana, while others live in cramped Soviet-era housing.
Polls show Rama winning more than 40 per cent of the vote, a commanding lead over Berisha, who has been weakened by graft charges.
But he could need help from smaller parties to maintain a slim four-seat majority in the 140-seat house.
"I will vote for new politicians because those like Rama and Berisha have been here for three decades and they only replace themselves," said Arber Qazimi, 21.
An economics student called Erisa said she would not even vote and was instead looking for a way to join the hundreds of thousands of Albanians who have emigrated in the past decade, many of them to nearby EU countries.
Others voted for something new.
"We want to see changes to stop youth from going out of the country," said Elson Toska, 37, after voting.
"The future is not Europe, to go and work there. We have our own country."
By some measures, Rama has done well. Annual economic growth above four per cent for 2022-2024, driven by trade with the EU and a tourism boom, outstripped other Balkan countries, the World Bank says.
But corruption remains a huge problem, experts say, driven by criminal gangs who make billions of euros from drugs and weapons trafficking overseas and bring it back to Albania to be laundered.
