Six models of meso-microporous materials having both micropores and mesopores are numerically constructed. Effective diffusion coefficients for these models are predicted by the volume averaging method. Solute diffusion coefficient in mesopores is assumed to be much larger than that in micropores. Effects of equilibrium distribution constant, the ratio of diffusion coefficient in mesopores to that in microporous regions, mesopore shape and mesoporosity on the diffusion enhancement originating from mesopores are discussed. It is found that the diffusion enhancement decreases with the increasing equilibrium distribution constant, and increases with the increasing mesoporosity and the ratio of diffusion coefficient in mesopores to that in microporous regions. The influence of the mesopore shape on the diffusion enhancement is obvious when the solute equilibrium distribution constant is small, but the influence decreases with increasing equilibrium distribution constant. A prediction of the diffusion enhancement based on the effective medium theory agrees reasonably with current numerical results.