The incident took place on the Farakka Express train near Dasrathpur halt in the district, police official Uma Shankar Prasad said.
"Unidentified criminals shot two SAP (Special Auxiliary Police) personnel after a heated exchange of words over a minor dispute about an open door," Prasad said.
"One of the personnel died on the spot while the other was admitted to a hospital in critical condition," he added.
Officials said the killing of the personnel of the Special Auxiliary Police unit under the state police created panic among the train passengers.
Last week, armed criminals had looted cash and valuables worth lakhs from passengers on a train in Saharsa district and shot at a passenger who resisted.