The incident happened inside the CISF camp at the Kolkata Port Trust (KoPT).
"We have arrested a CISF jawan after he gunned down inspector Gurupada Sheet," deputy commissioner of police (Port) V Nesakumar said.
According to police, the trooper fired three rounds from his rifle after a heated argument with the inspector, killing him on the spot.
He later surrendered and was arrested.
The accused will be produced in court later on Sunday.