This paper presents an advanced GM(1,1) model which can improve the accuracy of the conventional grey prediction and applies it to discrete sliding-mode control (DSMC). Using a Lagrange polynomial to take as a compensator and combining it with the original GM(1,1) model, the proposed prediction method can decrease the prediction error and easily implement in microprocessors with less computing time and memories. Then we employ this technique in DSMC to detect the system unknown perturbation. Comparing with the conventional DSMC, the proposed algorithm can reduce the switching gain and result in that the system state is bounded in a smaller region. Numeric simulation results of a DC motor are given to illustrate the feasibility and successfulness of the proposed design.