The party of President Paul Kagame had 42 of the 53 directly elected seats in the outgoing parliament.
Helped by quotas, Rwanda is the world’s only parliament where women form a majority.
The polls come days after two people were killed in two grenade attacks in the capital, Kigali.
No group has said it carried out the attacks but officials have blamed the rebel Democratic Forces for the Liberation of Rwanda (FDLR), which is accused of links to the 1994 genocide.
The Rwandan Patriotic Front (RPF) government has been praised for maintaining stability and overseeing rapid economic growth since the slaughter of some 800,000 minority ethnic Tutsis and moderate Hutus.
But President Kagame has been increasingly accused of ignoring human rights and stamping out any opposition.
Three other parties are contesting the poll, two of which are seen as close to the RPF.
Officials of the fourth party, PS-Imberakuri, have told the BBC that their supporters have been harassed during the campaign – charges rejected by the RPF.
Another party, the Unified Democratic Forces, has not been able to register for the polls.
Its leader Victoire Ingabire was convicted of terrorism last year – charges she says were politically motivated.
The BBC’s Prudent Nsengiyumva in Kigali says there were long queues when polls opened at 07:00 local time (05:00 GMT) as people wanted to vote early before going to work.
He says the queues have now died down.
The streets of the capital, however, remain quiet with many shops closed while workers are at the polls, our correspondent says.
Twenty-four of the 80 seats are reserved for women, young and disabled people.