In a fuel cell system, a start-up combustor (10) combusts a gaseous mixture of fuel supplied by an injector (15) and air supplied from a valve (12C) at a rich air-fuel ratio, and supplies high temperature combustion gas to a reformer (3) in order to activate the reforming catalyst. After completion of activation, the controller (50) stops supply of air by the valve (12C) and thereafter stops the fuel supply by the injector (15). During this delay period, combustion of fuel using residual air is performed at a rich air-fuel ratio by increasing the fuel supply amount of the injector (15). Thus it is possible to prevent temperature increase of the combustion gas as a result of the gaseous mixture approaching a stoichiometric air-fuel ratio after stopping fuel supply.