A police officer and another person were injured in the attack, The Hindu reported.
The Maoists were passengers on the 13235 Sahibganj-Danapur Inter-city train.
Amitabh Kumar Das, Railway Police superintendent in Jamalpur, said they attacked the train's police escort between Jamalpur and Ratanpur stations at around 6 p.m., opening fire on the police escort and grabbing their weapons.
Ashok Kumar, a head constable with the Bihar Military Police, and Uday Kumar and Bhola Kumar, Railway Police constables, were killed.
A Maoist attack in June on an intercity train between Dhanbad and Patna killed three people and injured six.
Workers migrating from Bihar, on India's northeastern border, to other parts of India often face discrimination.
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