An apparatus and method for diagnosing a fuel cell diagnoses a state of a fuel cell by estimating a fuel-cell equivalent circuit. The apparatus for diagnosing a fuel cell includes: an impedance measurement unit configured to measure impedance of a fuel cell within a predetermined frequency range; an equivalent circuit model unit configured to derive each parameter value by estimating a predetermined fuel-cell equivalent circuit model in response to the impedance received from the impedance measurement unit; and a fuel-cell-state diagnosis unit configured to diagnose a state of the fuel cell by detecting a variation of the parameter value derived from the equivalent circuit model unit.