Opposition leaders have called for a boycott after a number of protesters died in clashes with security forces.
Under the country’s current constitution, Denis Sassou Nguesso cannot seek re-election because he is over the age of 70 and has already served two terms.
Denis Sassou Nguesso first came to power in 1979.
He is now coming to the end of his second seven-year term.
Denis Sassou Nguesso won the last election 2009 with nearly 79% of the vote in a poll boycotted by half the opposition candidates.
Tens of thousands of people took part in a peaceful demonstration against the referendum in September.
Four people died on October 20, when security forces dispersed further protests in the capital Brazzaville and the economic capital Pointe-Noire.
Several activists and opposition leaders reported arrests and intimidation.
The outcome of today’s vote and the Congolese people’s response to it will be watched closely in the region, as presidents in the neighboring Democratic Republic of Congo and Rwanda are also expected to try to run for third terms in forthcoming elections.
There have been months of unrest in Burundi, where President Pierre Nkurunziza was re-elected for a controversial third term in July.
Among the changes being voted on are scrapping the presidential age and two-term limits.
Texting and internet services were cut and public meetings banned ahead of the referendum, residents said.
Congo-Brazzaville opposition has been campaigning under the slogan “Sassoufit”, a pun on the French expression for “that’s enough” (Ca suffit).
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