The invention discloses a motion planning system and method of an industrial robot for smoothly grabbing a moving object. The motion planning system of the industrial robot for smoothly grabbing the moving object comprises a smooth grab model building module, an obstacle avoidance algorithm module and a smooth grab algorithm module. The smooth grab model building module is used for describing the relative relationship between the target position and an end actuator and the relationship between an obstacle and the arm plane of the industrial robot so as to generate an attraction vector and a rejection vector. The obstacle avoidance algorithm module is used for generating the motion for avoiding the obstacle so as to avoid the moving obstacle. The smooth grab algorithm module is used for generating the smooth grab motion according to a smooth grab algorithm in the mode of using the attraction vector and the speed of the moving object as the input under the condition that the obstacle leaves from a collision-free region, so that the smooth grab operation is achieved. By the adoption of the motion planning system and method of the industrial robot for smoothly grabbing the moving object, the purpose that the industrial robot smoothly grabs the moving object in the working space in the complex industrial environment can be achieved, and therefore the damage to the object to be grabbed is avoided.