We prove in this paper the convergence of Adomian method applied to linear or nonlinear diffusion equations. The results show that the convergence of this method is not influenced by the choice of the linear inversible operator L in the equation to be solved. Furthermore we give some particular examples about a new canonical form where the initial value u 0 of Adomian series is chosen in some special form which verifies the initial and boundary conditions. Then Adomian series converges to exact solution or all approximated (truncated series) solutions verify these conditions.