Abstract: It is well known that lattice Boltzmann methods(LBM) make great success in many computational physics fields,expecially in fluid mechanics.A lattice Boltzmann method with BGK model is developed to solve Burgers equation.Detailed analysis shows that the calculating scheme is a three level nonlinear finite difference one.The maximum value principle has been proved and the existence,uniqueness and stability are also discussed.The computational results agree with second order finite difference solutions very well.