The last time the NLD contested elections in 1990, it won a landslide victory that was later disqualified by the military - with dissidents including Suu Kyi arrested or exiled.
The polls opened at 6 am (2330 Saturday GMT) and will close at 4 pm (0930 GMT).
The main opposition against the NLD are the army-backed Union Solidarity and Development Party (USDP) that has ruled the country for the last five years.
The USDP won the last election in 2010 - a poll that was boycotted by the NLD over prohibitive election laws.
The USDP have campaigned on a message of continuity and stability, arguing that they are the only party capable of tiptoeing the path to democracy under the watch of a weary and distrusting military.
"We must lead the country at least five more years so that the transition process stays peaceful," Hla Swe, a former army officer and a sitting member of parliament for the USDP.
The NLD have campaigned on a message of change, promising to reform the constitution and hasten the transition process.
Despite the lofty campaign promises, observers have been skeptical that the NLD will win the majority needed in parliament to bring about constitutional reform.