It is very important to understand stochastic diffusion of energetic charged particles in the nonuniform background magnetic field in plasmas of astrophysics and fusion devices. Using different methods considering an along-field adiabatic focusing effect, various authors derived a parallel diffusion coefficient and its correction T to , where is the parallel diffusion coefficient without an adiabatic focusing effect. In this paper, using the improved perturbation method developed by He & Schlickeiser and iteration process, we obtain a new correction to . Furthermore, by employing the isotropic pitch-angle scattering model , we find that has a different sign from that of T. In this paper, the spatial perpendicular diffusion coefficient with the adiabatic focusing effect is also obtained.