A failure diagnosis apparatus that includes an alternating current (AC) absorption unit that is connected to the fuel cell stack and switched based on an applied AC signal to enable a current from the fuel cell stack to flow. In addition, an AC signal generator is configured to generate the AC signal and supply the generated AC signal to the AC absorption unit. As the current from the fuel cell stack is absorbed by the AC absorption unit based on an alternating signal, a stack current input into a diagnosis processing unit includes an AC component, thus the diagnosis processing unit may diagnose fuel cell stack failure by analyzing a frequency of the AC component.