A device and a method for controlling a cold start of a fuel cell system are provided and are capable of increasing a fuel cell load to reduce a cold start time using a kinetic energy storage method for a rotor of a motor for driving a fuel cell system. The method improves cold start performance by performing self-heating of a fuel cell stack based on an increase in an output current amount of a fuel cell and by restricting a motor torque simultaneously with generating the motor torque while applying a current to a motor when a vehicle stops to consume an output current of the fuel cell.