Greenlanders went to the polls on Friday after their leader resigned early in October amid an expense scandal.
The campaign is mainly between the opposition party Inuit Ataqatigiit, led by Sara Olsvig, and the ruling social democratic Siumut party, led by acting Prime Minister Kim Kielsen, a former policeman.
Kielsen was in the post after Greenlandic Prime Minister Aleqa Hammond announced resignation as the chairwoman of the Siumut party on Oct. 1.
Hammond, who became the leader of self-governed Greenland after winning the 2013 general elections, was accused of spending around 106,000 Danish kroner (about 18,435 U.S. dollars) of public funds on private airline tickets and hotel stays for family members.
The fresh election is shadowed by the bleak economic reality as Greenland is struggling to capitalize on its potentially huge natural resources.
Greenland, an autonomous territory of Denmark, is sparsely inhabited with around 57,000 population. Greenland is largely self-governed, and Denmark maintains control only over foreign affairs and defense policy.
The Danish government subsidizes the island's economy, which heavily relies on fisheries, around 3.6 billion Danish kroner a year.
While the emancipation from Denmark was a hit topic in last year's election, in the run-up to Friday's vote it has been avoided by local politicians at a time when the autonomous government is relying more on the Danish subsidies due to declining mineral prices worldwide and a drop of its economy.
The gross domestic product in Greenland contracted 1.9 percent to 13.6 billion kroner in 2013, making the election campaign more focused on how to diversify the economy and boost its fishing revenues, which account for about 90 percent of its exports, and a nascent tourism industry.
"The status of Greenland's economy is very bleak, and going forward there is no indication that it will get better," Torben Andersen, the chairman of Greenland's Economic Council, was quoted by Danish news agency Ritzau as saying.
Friday's voting began at 0900 GMT, and the result of the election is expected to be ready early Saturday morning.