The impoverished west African country of 1.6 million is plagued by corruption and cocaine trafficking.
It is the first election since a coup in 2012, after which the EU and others suspended aid donations.
With a history of coups, no elected leader has served a full term since independence from Portugal in 1974.
A BBC reporter in the capital Bissau said turnout appeared to be high as he saw large queues at polling stations.
There were 13 candidates for president and 15 parties fielding candidates for parliament.
Among the presidential hopefuls are political heavyweights such as former Finance Minister Jose Mario Vaz, and Abel Incada, a member of the Party for Social Renewal (PRS) of former President Kumba Yala, who died last week.
The dark horse, however, could be 50-year-old independent candidate Paulo Gomes, an unusual proposition in a political landscape hitherto dominated by political grandees who made their names during the war of independence.
A gifted economist who has spent most of his life working abroad, including as the leader of the World Bank's sub-Saharan Africa division, he believes he has the know-how to begin to turn around the country's fortunes.
The west African nation has stagnated since 2012, under the rule of a transitional government backed by its all-powerful military.
With few resources other than cashew nuts and fish, South American drug cartels have turned the country into a cocaine trafficking hub.
The money that generates has corrupted many of the country's public institutions, particularly its armed forces.
A year ago, the US charged 2012 coup leader Antonio Indjai with drug trafficking and seeking to sell surface-to-air missiles to Colombia's FARC rebels, to shoot down US patrol helicopters. He has not been extradited.
Polling was monitored by 550 international observers and a presidential runoff is scheduled for 18 May if no candidate emerges as the clear winner.
The country is ranked 177th out of 187 in the UN's human development index, with two-thirds of the population living below the poverty line.
Voting has ended in presidential and parliamentary elections in Guinea-Bissau with no reported problems or incidents.