Some new Saul'yev type asymmetric difference schemes for Burgers'equation is given, by the use of the schemes, a kind of alternating group four points method for solving nonlinear Burgers'equation is constructed here. The basic idea of the method is that the grid points on the same time level is divided into a number of groups, the difference equations of each group can be solved independently, hence the method with intrinsic parallelism can be used directly on parallel computer. The method is unconditionally stable by analysis of linearization procedure. The numerical experiments show that the method has good stability and accuracy.