In order to promote the work efficiency, energy consumption and the smoothness of the manipulator, a mathematical model of quantic non uniform rational B-spline curve (NURBS) was set up to find trajectory with high-order of which endpoint parameters was specified. A hybrid particle swarm optimization algorithm ( HPSO) was used in the MATLAB simulation to get the perfect Pareto solutions under three normalized weighted objectives for six-degree freedom manipulator’ s trajectory. Through the simulation, it shows that the quantic NURBS curve can be constructed to fitting high order trajectory and the HPSO algorithm can provide a good means to get the Pareto solutions for the trajectory described above.