An inquiry has been made into the difference method for the initial boundary value problem of one-dimensional nonlinear variable coefficient Burgers equation. Firstly, by using the difference method, a two-layer nonlinear difference scheme has been established, followed by a proof of stability and convergence under appropriate conditions to be possessed by the proposed difference scheme. Finally, the effectiveness of the differential method constructed in this current research can be verified through specific numerical examples. The results indicate that the differential scheme is characterized with second-order accuracy in both space and time, thus demonstrating its advantages in computational accuracy, stability, and other aspects.