The closed-chain legged walking mechanism is characterized by high stiffness, strong load-bearing capacity, high driving efficiency, and simple control, which has attracted extensive attention. To further enrich the design ideas of such mechanisms, taking the four-bar mechanism as an example, a synthesis method for path generation based on multi-objective optimization is proposed. The kinematic constraint equations of the four-bar mechanism are established to obtain the motion trajectory of the end effector. Based on the performance requirements of the walking mechanism, the motion trajectory's length and height are defined, which are set as the optimization objective. The coordinates of the joints of the mechanism are selected as design variables, the optimization mathematical model is established, and a multi-objective optimization algorithm is applied to do the optimization. At last, a multi-legged closed-chain legged robot was determined based on the proposed method. The robot is driven by two motors and can achieve the motion functions, such as walking, turning, and obstacle avoidance, which can verify the effectiveness of the method.