A recent opinion poll gave her 60 per cent support and her closest rival, Algirdas Butkevicius, the leader of the opposition Social Democrat Party, just 8.4 per cent.
However, if she fails to gain 50 per cent of the vote on Sunday, Grybauskaite could still face a second round run-off to become the country's first female president.
If less than 50 per cent of Lithuania's 2.7 million eligible voters turn out, a candidate needs backing from a third of all eligible voters.
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.
"We need new ideas, we need someone to inspire the people to be more optimistic"
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.