A rope-driven parallel robot is a type of parallel robot which uses multiple ropes or cables to drive and control the movement of the end effector. How to reasonably plan the rope-driven parallel robot under the constraints of the unidirectional force of the rope and the range of the force-feasible workspace is a difficult problem. In view of this, a multi-objective trajectory planning method for a rope-driven parallel robot based on a cooperative game GA(genetic algorithm) was proposed. On the basis of establishing the kinematic and dynamic models of the rope-driven parallel robot, a multi-objective trajectory optimization model was constructed. GA was used to search the strategy space of each target player in the cooperative game, and a strategy combination that minimizes the overall utility was found in the strategy space of the game through the Nash negotiation solution. The experimental results show that the multi-objective trajectory planning method proposed satisfies the physical constraints and spatial constraints in the robot's trajectory motion at the same time, reduces the influence of energy consumption and impact force on the rope-driven parallel robot, improves the smoothness of the trajectory, and provides a reliable trajectory planning method for the efficient and stable operation of the rope-driven parallel robot.