Crank-Nicolson method is a finite difference scheme used to solve the heat and other parabolic partial differential equations. In order to solve the Burgers’ equation which is parabolic partial differential equations, an invariant numerical scheme, based on Crank-Nicolson method and discrete symmetries of Burgers’ equation, is established here. A comparison of the proposed numerical scheme with the Crank-Nicolson method and the exact solution is also presented. It is clearly observed that the convergence and performance of the modified Crank-Nicolson is better than that of the Crank-Nicolson method.