Provided is a fuel supply control device that performs power supply control of a shut-off valve including a first valve body that is disposed at a fuel supply path ranging from a gaseous fuel tank to a regulator and is opened in advance during power supply, and a second valve body that is opened due to a decrease in a differential pressure between upstream and downstream after the first valve body is opened, and fuel injection control. The fuel supply control device includes a control unit that sets a delay time from an initiation time of power supply to the shut-off valve to an initiation time of fuel injection in correspondence with a first fuel pressure upstream of the shut-off valve and a second fuel pressure downstream of the regulator, and initiates fuel injection after the delay time has passed after the initiation of the power supply to the shut-off valve.