The election commission has said that turnout is expected to be about 51 per cent.
Grybauskaite had been widely tipped for victory with the country in a deep recession and widespread public disenchantment with politicians.
"Our local political establishment is so boring for people, and they want to see some new faces," Grybauskaite said after voting in the capital, Vilnius, on Sunday.
"In the difficult times I can give my experience, my knowledge to my country."
Algirdas Butkevicius, the leader of the opposition Social Democrat Party, had trailed far behind Grybauskaite in opinion polls ahead of election day and exit polls indicated he had just 11.8 per cent of the vote.
"We need new ideas, we need someone to inspire the people to be more optimistic"
Grybauskaite, a former Lithuanian finance minister, has said the Baltic state must stabilise its public finances, stimulate exports, absorb EU aid faster and provide tax breaks for small and medium-sized businesses to tackle the economic downturn.
She entered the presidential race in February, after public anger over the economic situation erupted into a riot outside parliament.
The government has slashed public spending, but unemployment is climbing and the economy is forecast to shrink by 15.6 per cent this year.
"We need new ideas, we need someone to inspire the people to be more optimistic. The mood is quite gloomy at the moment," Elena Juozapaitiene, a student, told the Reuters news agency on Sunday.
Vytautas Vaigauskas, another voter, said: "I hope that a new president produces order, because now the situation is quite forlorn. It seems that I'm not the only one who'll be waiting for better policies."
Lithuania's president appoints the prime minister and cabinet.
The president also has some influence over economic policies, including the right to veto budget laws, but presidential executive powers are limited to implementing foreign and defence policies together with the government.