Grid point technique is a classical method in computing satellite constellation coverage to the ground regions. Aiming at improving the low computational efficiency of the conventional method, a method using latitude stripe division is proposed, which has high efficiency, and we name it latitude stripe method. After dividing the target region into several latitude stripes, the coverage status of each latitude stripe is computed by means of the spherical geometry relationship in the first orbital period. The longitude coverage intervals in the remaining orbital periods are computed by sliding the coverage status in the first orbital period. Based on this method, the instantaneous and cumulative coverage in simulation time can be calculated more efficiently. As well, the relationship between the cumulative coverage and altitude can be computed fast by this method, which could be used in the optimized design of repeating sun-synchronous orbits. The comparison between the conventional grid point method and the latitude stripe method shows that the latitude stripe method has high efficiency and accuracy. Through various case studies, the optimization in repeating sun-synchronous orbits design is successfully represented.