Votes will be cast to pick authorities that will run 61 districts across the country for the next four years.
While the Socialist-run government is insisting on holding the election, the opposition wants to stop it taking place. The opposition, led by the center-right Democratic Party, blames a corrupt government linked to organized crime and is demanding fresh national elections.
Albania's President Ilir Meta is sympathetic to the opposition and declared that the vote is canceled, but the government under Prime Minister Edi Rama has refused to abide by that decision.
On late Saturday the Democratic Party's leader Lulzim Basha called on Albanians to boycott the vote and said they would hold non-violent protests. Police have said protests are not allowed the voting day.
The ruling Socialists are the only candidates in 35 out of 61 districts, with some smaller leftist and center-right parties running against them in the rest.
Voting ends 1700 GMT. Preliminary election results are not expected until Monday.
Thousands of police officers guarded the polling stations Sunday. The Organization for Security and Cooperation in Europe's Office for Democratic Institutions and Human Rights said it was sending 174 election observers, who will give their preliminary findings on Monday.
Holding a free and fair election is considered key for the launch of EU membership talks for the tiny Western Balkan country, already a NATO member.