Conventional chaotic optimization is a sensitive initial values algorithm with low search accuracy and slowness of convergence. Besides, convergence of harmony search algorithm is not stable and its adaptability for the multi-objective optimization problems is poor. Therefore, a multi-objective hybrid algorithm based on parallel chaos optimization and harmony search algorithm (MOCOHSA) is proposed in this paper. In the MOCOHSA, the global search ability of parallel chaos optimization and local search ability of harmony research are utilized, and adaptive operation is introduced in the harmony search algorithm. In this way, the MOCOHSA has good search speed and convergence performance for multi-objective optimization problems. The proposed algorithm performs better than other multi-objective optimization algorithms for the optimization of 8 multi-objective optimization test functions. Finally, the algorithm is used to solve the satellite heat pipe design problem.