A Linear method is constructed for numerical solution of two dimensional non-linear Burgers equation. The scheme is derived from Crank-Nicolson finite difference scheme for linear terms and averaging for nonlinear terms. The method is shown to be consistent and second order accurate in time and space. The numerical solutions are obtained for two test problems at different time t and Reynolds number Re. The numerical solutions are compared with exact solution and other existing methods. Though the method is linear numerical solutions are compatible with ADM and Crank-Nicolson method