Nine candidates are taking part in Sunday's vote, which could require a runoff in two weeks' time.
The leading candidates include Prime Minister Saulius Skvernelis, former banking economist Gitanas Nauseda and former Finance Minister Ingrida Simonyte, AP reported.
The campaign has focused on domestic issues such as the economy, corruption and social welfare, even though foreign policy and defense are two of the presidency's main purviews.
Grybauskaite's anti-Russia views, no-nonsense style and karate black belt earned her the "Iron Lady" label previously applied to Margaret Thatcher when she was British prime minister.
Voters are also having their say in a referendum on a constitutional amendment to allow dual citizenship for hundreds of thousands of Lithuanians living abroad.