In this paper, we pe a new Divid-and-Conquer type method for the generalized discrete Sylveter equation :AXB + X = C,where the matrices A, B and C are large and sparse, and in addition, B is banded.This matrix equation arises in various applications in science and engineeing. In particular, a special form of the equation, namely, the diete-time Lyapunov equation :AXAT - X + C = 0arises in important control applications, such as stability analysis, balancing and model reduction. The standard numerical methods, such as the Hessenberg-Schur method, are not suitable for large-scale computing because the sparsity of the data matrices are completely destroyed. In last few years, Arnoldi and Lanczos-based Krylov subspace methods have been developed for large continuous and discrete-time Lyapunov, and continuous-time Sylvester equations. But no such methods have been published yet for the generalized Sylvester equation of the above type.The proposed method is of Divide-and-Conquer type and Arnoldi-basd. Thus it is suitable for both large-scale and parallel computations.The results of our numerical experiments show that the new method gives a satisfactory accuracy on relative residual error norms with several large and sparse test problems. On the other hand, the relative residual errors obtained by the existing Arnoldi-based method for the discrete-Lyapunov equation are not satisfactory at all, even for medium sized problems. More meaningful experiment and analysis with this new method are curntly underway.