In this paper, the energy-supplying capacity optimization of the cogeneration system based on a micro gas turbine (μ,GT)-solid oxide fuel cell (SOFC) hybrid system is discussed. The cogeneration system consists of the hybrid system, waste heat recovery devices and air-conditioning equipments. The power output capacity of the hybrid system is set in the range of 100kW to 800kW, because the floor area of a target building (hotel) is fixed at 7000m^2. Typical time-series energy demand data and the climate condition data in Tokyo are also used in the calculation. In consequence, the fuel consumption is approximately minimized at the power output capacity of 300kW. At this optimal capacity, the hybrid system should be operated under the partial load condition in order to follow the fluctuation of the electric power demand. The reduction of the fuel consumption becomes about 57% of a conventional energy supply system, and the energy cost saving is simultaneously reached to be almost 60%.