The present invention provides a solid oxide fuel cell system capable of preventing excess temperature rises while increasing overall energy efficiency. The present invention is a solid oxide fuel cell system, including: a fuel cell module, a fuel supply device, a heat storing material, and a controller which, based on power demand, increases the fuel utilization rate when output power is high and to lower it when output power is low, and changes the electrical power actually output at a delay after changing the fuel supply amount. The controller has a stored heat estimating circuit for estimating the surplus heat based on fuel supply and on power output at a delay relative thereto. When a utilizable amount of surplus heat is accumulated in the heat storage material, the fuel supply is reduced so that the fuel utilization rate increases relative to the same electrical power.