A numerical method of constant coefficient convection diffusion equation is studied. An implicit difference scheme is established for convective dominance and diffusion dominance respectively. Thetruncation error, convergence and stability of this scheme are discussed. Theoretical analysis and experimental results show that when the grid ratio is properly selected, the difference scheme is quite stable. It can be extended directly to the two-dimensional problem, and all the advantages of the difference scheme can be maintained. On this basis, an implicit split center difference algorithm is presented.