A method for operating a fuel cell power generation system is presented and includes sequentially resting fuel cell modules corresponding to a designated reference module number, from among all fuel cell modules of the fuel cell power generation system, during a designated number of cycles while operating remaining fuel cell modules, gradually reducing a number of the fuel cell modules sequentially rested during the cycles from the reference module number, whenever average performance of the fuel cell modules is sequentially reduced by exceeding designated reference levels configured to be sequentially set, and repairing or replacing the fuel cell modules when the average performance of the fuel cell modules is reduced by a designated lower limit or more.