"The voting is going on peacefully in all parts of the constituency," Jt Commissioner of Police (Headquarters) Jawed Shamim said.
The by-election will see a direct contest between the ruling Trinamool Congress and CPM.
The fight will be between Trinamool"s state president Subrata Bakshi and Ritabrata Banerjee of CPM. Besides, there are three Independents also in the fray in the constituency, which has an electorate of 15.6 lakh.
BJP and Trinamool"s ally Congress have not put up candidates. The seat fell vacant after Banerjee resigned as MP and successfully fought the Assembly by-election from Bhowanipore for her maiden entry into the state legislature.
The constituency is locally known as the chief minister"s pocket borough — Banerjee has won from here six times in a row since 1991.
Adequate security arrangements have been made for the by-election.
“Around 20,000 personnel have been deployed to ensure a free and smooth election," state Chief Electoral Officer Sunil Gupta said.
The polls, which are being held over seven Assembly segments constituting the Lok Sabha seat, began from 8am and would end at 5pm, he said.
Of the total 1,902 booths, 325 have been declared sensitive and 335 hypersensitive, the CEO said, adding there are three election observers.
Gupta said that 118 sector officers would oversee the security in the constituency.