The present disclosure relates to an apparatus and method for diagnosing a failure in a fuel cell system. To prevent degradation of a fuel cell stack due to abnormal supply of hydrogen, the apparatus includes a first pressure sensor that measures pressure of hydrogen supplied into the fuel cell stack, a second pressure sensor that measures the pressure of the hydrogen supplied into the fuel cell stack, and a controller that first diagnoses a supply state of the hydrogen based on a first pressure value measured by the first pressure sensor and a second pressure value measured by the second pressure sensor, and further diagnoses the supply state of the hydrogen based on an absolute value of a difference between the first pressure value and the second pressure value.