Proposed are a fuel cell system and a method of controlling the fuel cell system. The fuel cell system includes: a hydrogen supply unit connected to a hydrogen inlet side of a fuel cell stack, with a supply valve and a sensor being provided in the hydrogen supply unit; a hydrogen discharge unit connected to a hydrogen outlet side of the fuel cell stack, with a water trap and a purge valve being provided in the hydrogen discharge unit; and a controller configured to calculate an amount of hydrogen discharged through the purge valve from an amount of hydrogen supplied to the fuel cell stack and an amount of hydrogen consumed therein, and to perform compensation control of the supply valve when the amount of the discharged hydrogen is at or above a reference value.