Polls opened at 8:00 am (0000 GMT) amid rain showers and will close at 8:00 pm. The winner is expected to be known within hours after voting centres close.
Three months after a parliamentary election eroded the dominance of the People`s Action Party (PAP), which has ruled since 1959, anti-government sentiment is still running high in the online forums that now shape political debate in Singapore.
Four candidates -- all of them formerly associated with the government or civil service during their careers -- are running as individuals in the non-partisan contest, and there are around 2.3 million eligible voters.
"They are all very good candidates," auditor Andrew Ong, 26, told AFP after casting his vote.
Civil servant Mohamed Sadiq, 30, said he voted for "somebody who wouldn`t divide Singaporeans."
The publication of pre-election survey results is banned but former deputy prime minister Tony Tan, 71, who quit the PAP in June, is seen as the man to beat.
The three other candidates are former legislator and ex-PAP member Tan Cheng Bock, former insurance cooperative boss Tan Kin Lian and former corporate executive Tan Jee Say, who also worked in the civil service.(*)