Nicolas Maduro, who became president after the death of his mentor Hugo Chavez in 2013, will be seeking a third consecutive term, BBC reports.
His main challenger is Edmundo Gonzalez, a former diplomat who enjoys the support of a coalition of opposition parties.
Polls suggest Mr Gonzalez has a big lead over the incumbent president. However, as Mr Maduro's re-election in 2018 was widely dismissed as unfree and unfair, there are fears that the outcome of this election could be manipulated if it does not go in Mr Maduro's favour.
These fears are heightened by the fact that Maduro told his supporters that he would "win by tricks or scams".
After voting early in the capital Caracas on Sunday (28 of July), Maduro vowed to make sure the results announced by the National Electoral Council (NEC) were respected.
The NEC - the body that organises the elections and announces the official results - is dominated by members loyal to the government.
Its president, Elvis Amoroso, is a close personal ally of Maduro.
"The word of the electoral judge is sacred," the country's current president added.
Venezuelans began turning out to vote before 06:00 local time, when voting was due to start, and huge queues formed at polling stations across the country.
Tensions rose outside a polling station in Caracas where queuing voters clashed as they waited for the doors to open.
There are only a very limited number of independent observers in the country monitoring the elections - four from the UN and a small technical team from the Carter Center.
The invitation for observers from the European Union was withdrawn by the head of the electoral body, who is a close ally of Mr Maduro.
The former President of Argentina, Alberto Fernandez, was also not invited, having said that the Maduro Government should accept a possible defeat in the elections.
However, Maduro welcomed hundreds of guests from countries allied to his government, who he said would 'accompany' the vote.
In the meantime, the opposition has mobilised thousands of people who will act as witnesses at the various polling stations.
Despite the many obstacles the opposition has faced - including the constant harassment and arrest of more than 100 people linked to its campaign since the beginning of the year - the opposition sounds optimistic.
It claims that opinion polls give its candidate such a big lead over President Maduro that it will be impossible for him to steal the election.
The government rejects the opinion polls cited by the opposition, claiming that their candidate is in the lead.
Mr Maduro himself has resorted to harsh words in the run-up to the elections, warning of a 'bloodbath' if he is defeated.
That statement brought him a rare rebuke from Brazilian left-wing leader Luiz Inacio Lula da Silva, who said Mr Maduro should learn that 'if you win, you stay in power, and if you lose, you go'.
Mr Maduro has used the image of a struggling rooster as a symbol of his campaign and has adopted a combative attitude. | BGNES