In this paper, a class of successive permutation iterative methods for solving three-dimensional diffusion equations is constructed based on full-implicit discretization. The growth matrix of the method is given in this paper, and the convergence is analyzed. The new method can avoid solving large linear equations, and thus significantly improve the calculation speed. Compared with the full-implicit method and the Gauss-Seidel method, the new method not only has the same approximate accuracy as the full-implicit method but also is faster and more accurate than the Gauss-Seidel method.