This paper addresses capacity expansion planning model of distribution center with expansion size constraints. For discrete and finite time periods, demands for distribution center increase dynamically. The capacity expansion planning is to determine the capacity expansion size of private distribution center with expansion size constraints for each period through the time periods. The usability of public distribution center is considered strategically for capacity expansion of distribution center to minimize the costs. The cost factors are capacity expansion cost and excess capacity holding cost of private distribution center, and usage cost of public distribution center. Capacity expansion planning of minimizing the total cost is mathematically modelled. The properties of optimal solution are characterized and a dynamic programming algorithm is developed. A numerical example is shown to explain the problem.