According to opinion polls, a broad opposition coalition could capitalize on widespread frustration over food shortages, inflation and crime.
Nicolas Maduro’s governing PSUV, however, retains wide support in rural areas, and will continue to control the presidency.
Voters will be electing all 167 National Assembly members.
Even if the opposition Democratic Unity Roundtable captures a majority in the assembly, its power will be limited.
However, a win for the coalition – which includes center-left and centre-right groups – could mark a potential political shift in Venezuela.
The elections are widely regarded as a referendum on President Nicolas Maduro, the handpicked successor of the late president Hugo Chavez, and the party’s socialist policies.
The opposition accuses the United Socialist Party of Venezuela (PSUV) of mismanaging the economy and of squandering the country’s oil wealth.
Nicolas Maduro says his party defends the interests of ordinary Venezuelans and wants to complete Hugo Chavez’s “Bolivarian Revolution”.
“They say they’re winning in the polls – it’s the same story of the last 17 years,” Nicolas Maduro said at one election rally.
“Let them win in the polls, we will win in the streets.”
Among the concerns are chronic food shortages of staples – such as milk, rice, coffee, sugar, corn flour and cooking oil.
Nicolas Maduro has blamed the situation on an “economic war” waged against his government by the opposition.
The opposition also accuses the government of increasing authoritarianism.
Earlier this year opposition leader Leopoldo Lopez was given a 13-year prison sentence for inciting violence – a charge critics say was politically motivated.
Venezuela has invited election monitors from regional body UNASUR but has rejected those from the Organization of American States (OAS) and the EU.
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