In order to improve the working efficiency and stability of industrial robots,the trajectory of the robot is optimized. In the robot task space,the NURBS curve is used to describe end effector trajectory,the algorithm of the inverse kinematics of the robot is used to transform the task space trajectory into the joint space.A constrained backbones multi-objective particle swarm optimization algorithm with adaptive penalty function is proposed to optimize the time,velocity,acceleration and jerk of the industrial robot. The algorithm uses the adaptive exponential penalty function to deal with the constraints,which help to guide the algorithm to enter the feasible area faster,and search better target value. Finally,the correctness and validity of the proposed algorithm are verified by robot machining experiment.