In recent years, many types of energy supply systems have come into use in various buildings for spaceheating/ cooling and hot water supply. Lifetimes of buildings are generally more than 60 years, but those of energy supply systems are around 15~25 years. Therefore, these systems must be renewed several times during lifetimes of buildings. In the study, this renewal planning problem is formulated mathematically as an optimization one, in which the objective function to be minimized is the average value of annual total cost during system's evaluation period. Namely, this optimization problem is formulated as a large-scale mixed-integer linear programming problem, and the programming language AMPL solver is adopted here as the solving tool to derive the numerical solution. 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 hybrid system. The analysis is particularly focused on the influence of initial system's difference on the renewal planning of energy supply system. Through this study, the following results are mainly obtained: a) If the initial system is gas one, it is better to renew it to the electrical one as soon as possible due to relatively low energy efficiency of gas utilizing pieces of equipment, the high price of gas input energy in Japan, and so on. b) If the initial system is electrical one, the optimal renewal year becomes relatively later year, because it is economically better to use the initially installed high efficiency system as long as possible. c) Theoretically, the hybrid system is of course the best renewal one. However, there is no economic difference between the hybrid and the electrical systems.