In this paper, a method of rationally determining an optimal renewal plan is proposed for energy supply systems based on the optimization approach. In the planning of this proposed method, it becomes necessary to consider many factors such as the deterioration of each pieces of existing equipment, candidate pieces of equipment with upgraded efficiency reflecting technology improvement in the proper renewal year, the structure of renewal system, and so on. It is also necessary to determine the system's operational policy to match energy demands, which change daily and hourly through the year. A numerical study is carried out for a hospital with the total floor area of 25 000m2, where electrical (e.g., heat pump) and gas (e.g., gas engine cogeneration) systems are compared together with their combination of gas and electricity driven equipment (hybrid) system. Through this numerical study, the following results are obtained: a) Theoretically, the hybrid system is, of course, the best renewal system. However, the economic difference between the hybrid and the electrical systems is very small. b) The gas system is worse economically than the electrical one relatively due to the low energy efficiency of the related equipment, the high price of energy, and so on.