The present invention provides an apparatus for controlling hydrogen supply of a fuel cell system and a method for controlling the same. The apparatus includes a jet pump, a proportional control solenoid valve, and a controller. The jet pump is disposed at the side of an inlet of a fuel cell stack and performs supply and recirculation of hydrogen into the fuel cell stack. The proportional control solenoid valve is connected to a hydrogen supply line and fluidly communicates with a nozzle inlet of the jet pump to control the hydrogen supply to the jet pump. The controller controls an operation of the proportional control solenoid valve according to a power of the fuel cell system. Here, the controller controls the operation of the proportional control solenoid valve according to a pulse flow control method at a low power section in which a current power is lower than a predetermined reference power.