A technique of diagnosing a fuel cell stack is provided. In particular, current and voltage of a fuel cell stack are measured during driving of a fuel cell vehicle and the current and voltage are sequentially stored. It is then determined based on the stored current whether the vehicle is being operated at constant current. Different factors are analyzed depending on whether the vehicle is being operated at constant current, and then it is determined whether the fuel cell stack is in a normal state. A moisture supply into the fuel cell stack is calculated if it is determined that the fuel cell stack is not in the normal state. Based on the calculated moisture supply, whether the fuel cell stack is in a dryout state is diagnosed.