To reduce operation frequency of a relay switch while preventing a situation that a driver unintentionally makes a vehicle travel when an engine is automatically restarted to prevent a situation of generating noise due to operation of the relay switch.

A control device of a starter motor includes first and second relay switches 29, 31 for connecting/disconnecting power supply to a starter motor 25, an automatic stop/restart means 91 for automatically stopping/restarting the engine 11, travel prohibiting means 12, 21 for prohibiting the travel of the vehicle 10, a second relay control means 94 for making the second relay switch 31 in a cut state when the travel of the vehicle 10 is not prohibited, and a switching prohibiting means 95 for making the second relay switch 31 in the cut state when switching prohibiting conditions are satisfied. The switching prohibiting conditions include a condition that the engine 11 is determined to be in a normal operation.