State government, the world's oldest democratically elected -Communist administration, of a Railway Minister MamataBanerjee of India led by the opposition is being challenged.
Elections were held in six phases. Votes counted up to May 13 are due.
Important state elections in India survey in a series is the latest.
Tamil Nadu and Kerala have been voting, north eastern state of Assam and Pondicherry region of Union completed in South Indianstates.
West Bengal is voting in elections being held in 54 constituenciesand 9.74 million voters are eligible to vote on Monday.
Paramilitary forces and state police a large number ofconstituencies where voting is being held, six districts of NorthBengal has been deployed to spread, to ensure the vote passesoff peacefully.
Ms. Banerjee, who led the opposition Trinamool Congress party's recent shortage of its economy by 90 million people of West Bengal has accused the Communist failure.
A high voter turnout is expected.