We consider a satellite mission scheduling problem, which is a promising problem in recent satellite industry. This problem has various considerations such as customer importance, due date, limited capacity of energy and memory, distance of the location of each mission, etc. Also we consider the objective of each satellite such as general purpose satellite, strategic mission and commercial satellite. And this problem can be modelled as a general knapsack problem, which is famous NP-hard problem, if the objective is defined as to maximize the total mission score performed. To solve this kind of problem, heuristic algorithm such as taboo and genetic algorithm are applied and their performance are acceptable in some extent. To propose more efficient algorithm than previous research, we applied a particle swarm optimization algorithm, which is the most promising method in optimization problem recently in this research. Owing to limitation of current study in obtaining real information and several assumptions, we generated 200 satellite missions with required information for each mission. Based on generated information, we compared the results by our approach algorithm with those of CPLEX. This comparison shows that our proposed approach give us almost accurate results as just less than 3% error rate, and computation time is just a little to be applied to real problem. Also this algorithm has enough scalability by innate characteristic of PSO. We also applied it to mission scheduling problem of various class of satellite. The results are quite reasonable enough to conclude that our proposed algorithm may work in satellite mission scheduling problem.