President Kagame's party is expected to win a comfortable victory
Rwandans have been voting in the second parliamentary elections since the genocide of 1994.
A BBC correspondent in the capital, Kigali, reported a lively atmosphere at the polling stations.
President Paul Kagame's Rwandan Patriotic Front (RPF) is expected to win a large majority in the poll.
Two other parties standing in the election have supported Mr Kagame, while most opposition groups are in exile and are not contesting the poll.
The BBC's Geoffrey Mutagoma in Kigali said queues of voters were getting longer as the day progressed, and that songs were being played on national radio encouraging people to vote wisely.
Voters were excited and said their voting rights had been respected, he reported.
As he cast his vote, President Kagame said the election would help entrench stability in the country.
"There is no doubt that RPF is confident of a win," he said.
But the United Democratic Forces, a group of Brussels-based exiled opposition movements, has strongly criticised the poll.
"So long as one political party, the RPF, monopolises all the state machinery, decides which party or individual can contest elections, seals off all the country during the electoral process, elections will amount to a smokescreen," the group said in a statement last month.
In the previous elections, in 2002, the RPF won almost three-quarters of the vote.
More than 4.7 million people are eligible to vote in the poll.
On Monday, voters are electing 53 parliamentarians, with 27 remaining seats to be allocated through indirect elections on 16-18 September.
Some 800,000 minority Tutsis and moderate Hutus were slaughtered by Hutu militias in just 100 days during Rwanda's genocide in 1994.
Mr Kagame was instrumental in establishing the Tutsi-led RPF - the rebel force which took power and ended the genocide.