In order to solve the influence of the time delay on remote control system, a new predictive system of remote-controlled mobile robot was proposed in the non-visual environment. The dynamic model of mobile robot was used as the basis, the Smith predictor was used to compensated the signal time delay between the controller and the mobile robot, reduced the positioning error caused by time delay. The grey predictor model was used to predict the value of the sensors on the mobile robot, thus reducing the remote control error caused by time delay to the operator. The feasibility of the algorithm was proved by simulation. And by the experiment of the force feedback device and the mobile robot in the non-visual environment, the feasibility of the system was proved. Although the human operator participated in the remote control experiment, the compensation effects had been clearly demonstrated.