Some 3.8 million people were eligible to vote at the 6,500 authorized polling stations, which began at 7 a.m. (local time) and will stay open until 7 p.m. (local time), Efe news reported.
Of the voters, about 1,77,000 live abroad and half in Bosnia, where ethnic Croats constitute one of the three official nationalities and can also vote in Croatia.
According to polling, only three of the 11 candidates look to be in the running to move on to the run-off - which will be held on January 5 - if none of them achieves an absolute majority Sunday.
Those in contention are current president, the conservative Kolinda Grabar-Kitarovic, ex-Prime Minister Zoran Milanovic, and independent candidate Miroslav Skoro, a popular folk singer and economist supported by the nationalist far-right parties.
Grabar-Kitarovic is a candidate of the ruling center-right Croatian Democratic Union (HDZ) and has been the country's first female President since 2015.
Milanovic is presented by the center-left Social Democratic Party, with the support of 12 other left-wing formations.
The latest polls put Grabar-Kitarovic and Milanovic as favorites with the number of those intending to vote for them at around 25 percent, while Skoro sat at around 23.7 per cent.
"We have pulled Croatia out of apathy and gloom. Croatia is no longer on its knees, it's upright. Croatia is again known in the world for its successes," Grabar-Kitarovic said at a campaign rally in Zagreb on Thursday.
The result of the elections, ahead of Croatia assuming the rotating presidency of the European Union for the first time on Jan. 1, could influence the general elections that the country will hold at the end of next year.
Analysts agree that a victory by Grabar-Kitarovic would reinforce the position of the HDZ, which currently heads a minority government coalition.
The first partial official results are expected to be made public after 8 p.m. (local time).
( With inputs from IANS )