Voting began in the Russian far-east at 20:00 GMT on March 17, and opened in Moscow nine hours later.
The first results will arrive in the evening. Vladimir Putin has been Russia’s dominant leader since 1999, either as president or prime minister.
The incumbent president is hoping for another six-year term and faces seven other candidates.
Vladimir Putin’s rivals include a millionaire communist, Pavel Grudinin, a former reality TV host, Ksenia Sobchak and veteran nationalist Vladimir Zhirinovsky.
Alexei Navalny, the main opposition leader, has been prohibited from standing, because of a fraud conviction that he said was politically motivated.