The present invention provides a fuel cell power system, in which a combustion exhaust gas having a high temperature and generated by the combustion reaction of unreacted fuel gas and oxidizer gas which are not utilized in a power-generating reaction is introduced into a gas header for distributing the fuel gas or the oxidizer gas to a plurality of fuel cells contained in a fuel cell body, in such a way that a larger amount of heat is transferred to the gas which is to be supplied to the cells disposed in a peripheral area of the fuel cell body by heat exchange, and a smaller amount of the heat is transferred to the gas which is to be supplied to the cells disposed in a central area of the fuel cell body.