A multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is developed to solve Burgers equation. The general MRT-LB model can be thought as a three-level nonlinear finite difference scheme. Maximum value principle has been proved, and the existence, uniqueness, and stability parameters are discussed for the three-level finite difference scheme of MRT-LB model. Numerical stability analysis shows that the MRT-LB model is not only a three-level nonlinear finite difference one but also has the good numerical stability. Numerical solutions have been compared with the exact solutions and other LB models reported in previous studies. The experiments results show that the scheme is accurate and effective for Burgers equation.