An apparatus for converting power of a fuel cell for power generation to remove an open voltage of the fuel cell and a method thereof are provided. A controller links current to a system or load to reduce an open circuit voltage (OCV) of the fuel cell before power generation of the fuel cell is started, after the fuel cell is started. A power converter converts and supplies power generated by the fuel cell to the system or load. The apparatus removes an OCV of a fuel cell stack to prevent performance and life of the fuel cell from being reduced.