Polling stations were scheduled to shut at 18:00 local time (23:00 BST), but they have to remain open if people are still queuing to cast their vote.
Mr Maduro's main challenger is Edmundo González, a former diplomat who has the backing of a coalition of opposition parties.
The opposition called on supporters to keep vigil at polling stations in order to verify the counting process in the "decisive hours" after closing, amid widespread fears the PSUV would attempt to steal the vote.
Opinion polls have suggested Mr González has a wide lead over the incumbent.
This was reflected in the queue at one polling station in Petare, a poor neighbourhood of Caracas, where many people said they were voting for change.
Since he assumed the presidency in 2013, Mr Maduro has presided over an economic collapse, during which GDP shrank by 70% and more than 7.7 million people fled the country in search of a better life.
“This government has had all the opportunities to make Venezuela a great country, but instead we have misery,” voter Hector Emilio D’Avilia told the BBC.
One woman, Adriana Arreaza, said through tears that she just wanted “decent salaries for teachers and doctors, quality of life for the elderly and the youth, and a change for our country".
As Mr Maduro's 2018 re-election was widely dismissed as neither free nor fair, there is concern that the result of this election could be tampered with, should it not go his way.
Opponents of the president have overcome many hurdles in the run-up to the election, not least the fact that their chosen candidate, María Corina Machado, was banned from running for office.
Ms Machado, who has remained at the forefront of the opposition campaign, reminded voters that the counting process was legally meant to be public.
She called on "all Venezuelans to remain at their polling stations... keeping a vigil".
A community leader, Katiuska Camargo, told the BBC that the people of Venezuela were determined that the government "leave power immediately".
"There’s been outrage after outrage. Violations of human rights, extrajudicial executions, excessive emigration.”
The PSUV has been in power in Venezuela for the past 25 years - first under the late Hugo Chávez, then under his hand-picked successor, Mr Maduro.
Under their leadership, the PSUV has gained control not just of the executive and the legislative, but also of much of the judiciary.
The party has a core of loyal supporters who praise the "benefits" they say it has brought them.
Felix García said the Maduro government had provided “help for people like me with disabilities".
'By hook or by crook'
Mr Maduro has said he intends to win the election "by hook or by crook" and has warned of a "bloodbath" if he loses.
The National Electoral Council (CNE) - the body which organises the election and announces the official result - is dominated by government loyalists.
Its president, Elvis Amoroso, is a close personal ally of Mr Maduro.
Venezuela has the world's biggest oil reserves, but its oil output has plummeted under President Maduro - the result of a combination of lack of investment, mismanagement and oil sanctions.
A lifting of the oil sanctions - imposed by the US in order to exert pressure on Mr Maduro following the 2018 presidential election - could have repercussions on the price of oil globally.
Ione Wells in Caracas & Robert Plummer in London