A fuel battery system comprises a fuel battery stack, a hydrogen supply system for supplying hydrogen from a hydrogen tank, an oxidant gas supply system for supplying air serving as an oxidant by an air compressor, an electrical system including an impedance measuring unit for measuring the impedance of a fuel battery, a DC/DC converter for converting generated electric power, a secondary battery for storing electric power, and so on, and a drive system for driving a vehicle. When the power generation is stopped by turning off an ignition switch in the state in which the power generation is suspended in an intermittent operation, the impedance measuring unit measures the impedance after the supply of air is stabilized to avoid the transient state of the fuel battery cell caused by a delay in air supply.