The thermal and mass diffusivity in a porous medium of complex structure is studied by using the lattice Boltzmann method. The media under consideration include two-dimensional medium with an array of periodically distributed circular and square cylinders, three-dimensional granular medium of overlapping or non-overlapping spherical and cubical inclusions of different size, and randomly generated fibrous medium. The calculated effective diffusivities are in good agreement with existing analytical and numerical results when the inclusions, regardless of their shapes, are not overlapped. For the medium of overlapping inclusions, the effective diffusivity deviates from existing correlations as the inclusion fraction increases. In particular, the deviation increases dramatically if the thermal diffusivity of the inclusion is greater than that of the fluid in the medium for enhanced thermal conduction. A new empirical correlation between the effective diffusivity and the volume fraction for the medium of overlapping inclusions is proposed. (C) 2008 Elsevier Ltd. All rights reserved.