The voting began at 12,562 voting centers on Sunday at 6:00 a.m. local time (1030 GMT) and finished at 6:00 p.m. local time (2230 GMT) with a high turnout of about 70 percent. About 250,000 troops were on duty to ensure security.
Minutes after the official close of the polling stations, the PSUV claimed its victory although the national electoral council (CNE) said that the first results would be announced on Sunday night at 10:00 p.m. local time (0230 GMT Monday).
CNE president Tibisay Lucena said that in some states the voting centers were not closed at the established time as there were voters still standing in lines to cast the ballot.
Lucena also asked the candidates to wait peacefully for the official results.
Meanwhile, PSUV campaign chief Aristobulo Isturiz praised the voters for their enthusiasm in casting their ballots.
"We have an electoral system to be proud of and Armed Forces which know how to fulfill their military civilian tasks," he told a press conference.
Before the voting began, President Hugo Chavez said that as the world's eyes were on Venezuela, the elections were "very important."
More than 17.5 million people were registered to vote on Sunday for 165 lawmakers to the National Assembly and representatives to the Latin American Parliament.
The new lawmakers will take office on Jan. 5, 2011 for a term of five years.