A multi-stage optimal renewal planning problem for the energy supply system is studied by evaluating the long-term economics based on the annualized cost method. This problem is mathematically expressed as a mixed integer-linear programming formula, and a numerical study is carried out for an office building using the GAMS/CPLEX solver. Decision variables are the renewal year and the system's configuration at each of the renewal multi-stages together with the system's operational strategy for hourly changing energy demands. By taking the deterioration of the existing equipment of the system into account, the renewal system is assumed to be composed by adding the same and new types of equipment with technologically improved performance. The present planning year is set as 10 years after the system's initial construction, and the evaluation period is assumed to be 20 years from present, with the system renewed twice during this period. The main results are as follows: From the economic standpoint, the optimal first and second renewal years are the 10th and 22nd years after the system's initial construction. Comparing this optimal solution with the reference renewal plan, which renews the system using the same configuration only once, 15 years after the initial construction, the average annual total cost can be reduced 4.89 %.