A class of shock wave solutions of Zakharov-Kuznetsov-Burgers (ZKB) equation is obtained with hyperbolic-function-expansion method. Dynamical stability property of shock waves under transverse perturbations is investigated. Firstly, we made linear stability analysis on shock waves. A finite difference scheme with high accuracy is presented to solve numerically the eigenvalue problem. It shows that the shock waves are linearly stable with positive dissipation, while they are linearly unstable with negative dissipation. Secondly, a finite difference scheme is constructed to make long-time nonlinear dynamical evolution of shock waves. The results show that shock waves of ZKB equation are dynamically stable in the case of positive dissipation.