In this paper, we address a problem of designing satellite constellations to deal with a sequence of Earth revisit missions in the presence of limited resource capabilities. In order to fulfill the periodic coverage requirements, we take the repeating ground-track orbit into account and propose a semi-analytical method. After analyzing the coverage capacity of the resource for a random spot target on Earth’s surface, we define and calculate the feasible longitude interval of ascending node of the orbit. Subsequently, a mixed integer linear programming (MILP) model and an improved 0/1 programming model are formulated with coverage constraints that considerably reduce the size of the search space. We demonstrate that the new method significantly improves the optimization efficiency and verify the robustness of the solution.