The present invention provides a hydrogen supply system for a fuel cell which can compensate for a change in temperature, caused by heat generated when a high pressure tank is charged and discharged with hydrogen, using a metal hydride (MH) tank providing high hydrogen storage density, mounted in the high pressure tank such that hydrogen is to be discharged from the MH tank when hydrogen is charged to the high pressure tank, and hydrogen is to be charged to the MH tank when hydrogen is discharged from the high pressure tank.For this, the present invention provides a hydrogen supply system for a fuel cell, including: a high pressure tank which is capable of storing hydrogen received from a hydrogen refueling station and includes a metal hydride (MH) tank capable of storing hydrogen, mounted therein; first and second solenoid valves provided at both ends of the high pressure tank; a buffer tank connected in parallel to the high pressure tank; and a fuel cell stack connected to the buffer tank so that hydrogen from the high pressure tank or the MH tank is supplied to the stack through the buffer tank, wherein the hydrogen is charged from the hydrogen refueling station to the high pressure tank and discharged from the high pressure tank through the first solenoid valve, the hydrogen is charged and discharged to and from the MH tank through the second solenoid valve, the hydrogen is discharged from the MH tank as the first and second solenoid valves are simultaneously opened when the hydrogen is charged to the high pressure tank, and the hydrogen discharged from the MH tank is stored in the buffer tank and then supplied to the fuel cell stack.