Simultaneous by-poll is being held in the Kotulpur assembly constituency of Bankura district.
The area going to the hustings included the Maoist heartland of Junglemahal - the large forested stretches of West Medinipur, Bankura and Purulia districts - where a massive security cover has been provided.
"The average turnout was 61.62 percent till 1 p.m.," an official said here.
The average turnout in West Bengal was 61.62 percent till 1 p.m
An electorate of over 88.77 lakh, including 42 lakh women, is eligible to vote at 11,321 polling stations. Elections are taking place in Jhargram, Medinipur, Purulia, Bankura, Bishnupur and Asansol constituencies.
The political fate of 72 candidates is being decided. Eleven of the contestants are women.
BJP candidate from Asansol Babul Supriyo accused the ruling Trinamool Congress of indulging in "blatant rigging" and "intimidation of voters".
Additional security was provided to Supriyo, who is a Bollywood singer, after he was allegedly heckled and prevented from entering a polling booth by Trinamool activists.
The Opposition Left Front spearhead Communist Party of India-Marxist (CPI-M) alleged that its polling agents were beaten up and prevented from manning the booths in several areas.
There were also allegations that the Trinamool activists tried to forcibly prevent CPI-M supporters from voting in Jamuria in Asansol Lok Sabha constituency of Burdwan district.
The police intervened and took them to the booth.
In Pandbeshwar of Burdwan district, a physically challenged man was mercilessly beaten up by some goons backed by a political party after he cast his vote.
The Trinamool denied all allegations.
Trinamool activists surrounded ansd blocked the car of the Communist Party of India candidate from Medinipur, Prabodh Panda, outside a polling booth, alleging that the vehicle had MP's sticker.
The Trinamool, Left Front, Congress and the Bharatiya Janata Party are in fray in all the parliamentary constituencies that went to polls Wednesday.
Of the Left Front partners, the CPI-M is contesting four seats, leaving one each to the Communist Party of India and All India Forward Bloc.
In 2009, Left Front candidates bagged all the six seats.
Much interest has been generated among poll watchers by the Asansol seat where BJP candidate Babul Supriyo is giving a tough fight to Trinamool's trade union president Dola Sen and CPI-M's sitting MP Bansa Gopal Choudhury.
A stiff contest is on in Bankura where nine-time CPI-M MP Basudeb Acharia is being challenged by Trinamool's star candidate Moon Moon Sen, the actress-daughter of legendary Bengali film heroine Suchitra Sen.
The focus is also on Jhargram - for long the epicentre of Maoist violence - and Purulia and Bankura, parts of which are affected by the Left extremism.
Three helicopters, with a medical support team on board, have been pressed into service in the affected areas. Besides choppers, as many as 10 satellite phones are being used.
Central security forces have been deployed across all booths in the Maoist belt.
Bomb disposal squads, road opening parties and anti-landmine vehicles too have been deployed in the Maoist-affected areas.
West Bengal has 42 Lok Sabha seats, of which four voted April 17, six April 24 and nine April 30. Elections will be held for 17 constituencies in the final phase May 12.
Votes polled across the country would be counted May 16.