Dozens of people were queuing in Caracas neighborhoods including Chacaito and Los Palos Grandes before polling stations opened at 7:00 am (1100 GMT), according to the Democratic Unity Roundtable (MUD) opposition coalition.
They are due to close at 4:00 pm (2000 GMT), though they will remain open as long as there are people in line.
Delegates and volunteers, many dressed in white, manned tents and tables at some 14,300 polling stations nationwide.
The authorities have refused to greenlight a vote that has been presented as an act of civil disobedience and supporters of Maduro are boycotting it.
The vote is not binding because it lacks the backing of the National Electoral Council.
But voters in Sunday's election seemed set to reject the president's controversial plan for a separate referendum in two weeks to elect a citizens' body to revise the constitution.
The opposition has told its supporters to stay away from the Maduro-backed July 30 vote.
Opposition leaders like Henrique Capriles are expecting 11 million people to participate in Sunday's vote, which is intended to increase pressure to remove Maduro from power before his term ends in January 2019.
The rival votes have given rise to international worries - voiced by the Catholic Church and UN Secretary General Antonio Guterres - that the chances of bringing both sides together for dialogue have become more remote.
That in turn is stoking fears of more protests and running street battles with police, clashes that have cost the lives of nearly 100 people since the beginning of April.
Maduro portrayed the vote as merely an "internal consultation by the opposition parties" with no electoral legitimacy.
But he also urged Venezuelans to "participate peacefully."
