In recent years, nonlinear evolution equations with variable coefficients received more and more attention. (G′/G)-expansion method, a new method put forward by Wang Ming-liang et al in 2008 was applied to the nonlinear evolution equations with variable coefficients for the first time. The generalized Burgers equation with variable coefficient was taken as an example, and new exact solutions were obtained successfully when the coefficient meet the controlled conditions. When this expansion method was improved, the new solution of generalized Burgers equation with variable coefficients can be obtained successfully once again. It is proved that this expansion method is not only easy when solving nonlinear evolution equations with constant coefficients but also very efficient, concise and practical when solving the nonlinear evolution equations with variable coefficients, and it also has a broad application.