"Our people were on a routine search of trains and found the bombs in one of the trains," said Amarkanti Sarkar, Inspector General of Railway Police.
No one claimed responsibility for planting the bombs, and police said it was too soon to name a suspect.
The discovery comes days after a bomb went off in a mosque in the southern city of Hyderabad, killing 11 people.
The train was set to travel from the Howrah railroad station in Calcutta to Tarakeswar, a small town sacred to Hindus some 80 kilometers (50 miles) west of Calcutta. Hundreds of pilgrims use the train daily.
There have been several attacks on trains in the last year, including the July bombings of seven Mumbai commuter trains that killed more than 200 people, and the bombing of a train linking India and Pakistan that killed 68 people in March.
In January, an explosion ripped through two cars of a passenger train near Belacoba railroad station, about 550 kilometers (345 miles) north of Calcutta, killing four people.