In order to improve the motion performance of space manipulators, multiple objectives and constraints are required in operations on orbit. Based on non-dominated sorting genetic algorithm (NSGA-II), a method is proposed to achieve multi-objective trajectory optimization with multi-constraints. Considering the maximum speed and acceleration at the end-effector as decision variables, quantities of operation time and energy cost are treated as optimal goals. Moreover, multi-constraints of manipulator and the environment are introduced during the trajectory optimization. As a result, equations of multi-objective trajectory optimization are established. Then the Pareto optimal set of multi-objective optimization problem (MOP) is calculated, and the validity of the algorithm is verified with a seven degree-of freedom (DOF) space manipulator.