Voters are to choose a temporary 200-member assembly which will select a cabinet
Libyans are set to hold their first free election for more than 50 years, in a vote overshadowed by violence and deep national divisions.
They are selecting a temporary assembly which will have the task of picking a cabinet and a prime minister, reports the BBC.
An electoral worker died on the eve of the vote when gunmen attacked a helicopter near Benghazi.
Many people in eastern Libya are angry that they have been allotted only 60 seats in the 200-seat assembly.
Under the system devised by the outgoing National Transitional Council (NTC), which led the campaign against Gaddafi, 100 seats are allocated to the west and 40 to the south.
The BBC's Rana Jawad in Tripoli says some in the east fear being marginalised as they were for decades under Col Muammar Gaddafi's 42-year rule.
As many as five oil terminals have been shut down by former rebels, including those at Brega, Ras Lanouf and Sidra, and a significant part of Libya's oil exporting capacity has been disrupted.
Ballot papers were set alight at a key election office in Ajdabiya and another election centre was attacked in Benghazi.
In an attempt to defuse the situation, the NTC has said the new parliament will no longer be responsible for naming the panel that will draft Libya's new constitution.
The 60-member committee will be elected in a separate vote at a later date.
A Libyan army spokesman said the helicopter was transporting voting materials when it was attacked close to the airport in Benghazi. An election commission worker was fatally wounded, he said, but the helicopter managed to land safely.
An election commission member in Tripoli told the BBC that the identity of the gunmen was not yet known but that the attack would not affect the vote.
The poll has already been postponed once before.
Around 2.9 million people are eligible to vote for the 3,700 candidates standing for the new General National Congress, in Libya's first national vote since Col Gaddafi was toppled in October 2011 after an eight-month uprising.
There are countless political parties taking part in the election, our correspondent says, but the biggest to emerge so far is the Justice and Construction Party, made up mostly of Muslim Brotherhood members.