A fuel cell system having an adsorber placed in an air supply path to an air electrode of a fuel cell and receiving a chemical filter for adsorbing impurities contained in air; measurement means for measuring the amount per unit time of air having passed the adsorber; detection means for detecting the density of impurities contained in the air, whose volume has been measured by the measurement means, before it enters the adsorber; estimation means for estimating, based on the amount of the air, the density of the impurities, and adsorption efficiency of the chemical filter, the amount of the impurities adsorbed per unit time by the chemical filter; and output control means for causing a signal to output when an accumulated value of the amount of the impurity exceeds a predetermined level.