A new prediction scheme has been proposed for the robust teleoperation in a non-visible environment. The positioning error caused by the time delay in the non-visible environment has been compensated for by the Smith predictor and the sensory data have been estimated by the Grey model. The Smith predictor is effective for the compensation of the positioning error caused by the time delay with a precise system model. Therefore the dynamic model of a mobile robot has been used in this research. To minimize the unstable and erroneous states caused by the time delay, the estimated sensor data have been sent to the operator. Through simulations, the possibility of compensating the errors caused by the time delay has been verified using the Smith predictor. Also the estimation reliability of the measurement data has been demonstrated. Robust teleoperations in a non-visible environment have been performed with a mobile robot to avoid the obstacles effective to go to the target position by the proposed prediction scheme which combines the Smith predictor and the Grey model. Even though the human operator is involved in the teleoperation loop, the compensation effects have been clearly demonstrated.