The CPP currently has 73 seats, and party officials say they expect to win at least eight more.
More than eight million people are registered to vote. Official results could take days to be announced, but the parties are expected to release their own tallies by Sunday evening.
Allegations of voter intimidation had been made a day ahead of the poll.
Eleven parties are competing in Sunday's national poll, the fourth since the end of the civil war.
The opposition Sam Rainsy Party is expected to maintain its strength in the capital, but not in rural Cambodia, where most voters live.
Campaigning has been marred by accusations of intimidation and vote buying amid a heightened nationalist sentiment over a border dispute with Thailand.
Pung Chiv Kek, president of the human rights group Licadho, said that the election campaign did not bode well for the vote.
"We have 13 activists killed, including the journalist of the opposition newspaper, so this sends a very negative message to the voter," she said.
"We can hardly say that this election is free because there is still intimidation and physical abuse - this is the stick. The carrot is buying votes, building roads and schools.
"By using sticks and carrots, we are sure the ruling party will win a large majority."
The CPP is expected to win because opposition parties had not presented an attractive vision to the Cambodian people, Pung Chiv Kek told Al Jazeera.
"The opposition didn't manage to unify before the election, so their seats in parliament will be less," she said.
In the absence of a credible opposition, Pung Chiv Kek said, Cambodia will have more problems "of land grabbing, evictions, corruption, impunity, no independence of the judiciary".
Talks between Thailand and Cambodia on Monday failed to end a military stand-off over the disputed Preah Vihear temple on their border, recently listed by Unesco as a World Heritage site.
|Opposition leader Sam Rainsy, left, is facing prime minister Hun Sen [AFP]
Hang Puthea, head of the election monitoring group Nicfec, said campaigning had been largely overshadowed by concerns over the temple.
"People are more focused on the border issue at Preah Vihear temple than on the election," he told the AFP news agency.
Boonsrang Niumpradit, Thailand's supreme commander, said the objective of the talks was to allow soldiers to stay in their current positions at the temple, but avoid any confrontation.
Hun Sen has accused Thailand of ignoring international law and threatening regional peace by sending troops into the disputed zone around the temple.
Previous polls held in Cambodia have been marred by violence. Scores of people - mainly opposition supporters and activists - were killed or beaten in the run-up to elections in 1998.
Election monitors say political violence has diminished greatly compared to past polls. But unequal access to the media is still a problem.