Fuel cell system and method of operating fuel cell system

To improve economical efficiency, responsiveness and durability of a power generation system combining a fuel cell and secondary cell. (Constitution) A fuel cell system includes a fuel cell that supplies an oxidizer containing oxygen to a positive electrode, supplies a fuel gas containing hydrogen to a negative electrode and generates power, a battery containing at least water as an electrolyte, a hydrogen tank that stores hydrogen generated from the battery and a hydrogen pipe that supplies hydrogen in the hydrogen tank to the fuel cell.