Abstract: A characteristic finite analytic method is proposed to obtain the numeri cal solution of convective diffusion eguation. The scheme formed is unconditionally L_∞ stable and in accordance with the convective diffusion phenomenon in physics.In this paper the existence and uniqueness of the scheme is proved and the error estimate of the numerical solution for the linear and non-linear equation is given. The numevical experiment shows that the present method has the ability to simulate the convective diffusion equation with high order accuracy, Irttle numerical dissipation, perfect stability and without any parasitic osillation.