In this study, the system of 2-D Burgers equations is numerically solved by using alternating direction implicit method. Two model problems are studied to demonstrate the efficiency and accuracy of the alternating direction implicit method. Numerical results obtained by present method are compared with the exact solutions and numerical solutions given by other researchers. It is displayed that the method is unconditionally stable by using the von-Neumann (Fourier) stability analysis method. It is shown that all results are in good agreement with the results given by existing numerical methods in the literature.