Transport of conduction electrons and holes through the lattice of alpha-Fe(2)O(3) (hematite) is modeled as a valence alternation of iron cations using ab initio electronic structure calculations and electron transfer theory. Experimental studies have shown that the conductivity along the (001) basal plane is four orders of magnitude larger than the conductivity along the [001] direction. In the context of the small polaron model, a cluster approach was used to compute quantities controlling the mobility of localized electrons and holes, i.e., the reorganization energy and the electronic coupling matrix element that enter Marcus' theory. The calculation of the electronic coupling followed the generalized Mulliken-Hush approach using the complete active space self-consistent field method. Our findings demonstrate an approximately three orders of magnitude anisotropy in both electron and hole mobility between directions perpendicular and parallel to the c axis, in good accord with experimental data. The anisotropy arises from the slowness of both electron and hole mobilities across basal oxygen planes relative to that within iron bilayers between basal oxygen planes. Interestingly, for elementary reaction steps along either of the directions considered, there is only less than one order of magnitude difference in mobility between electrons and holes, in contrast to accepted classical arguments. Our findings indicate that the most important quantity underlying mobility differences is the electronic coupling, albeit the reorganization energy contributes as well. The large values computed for the electronic coupling suggest that charge transport reactions in hematite are adiabatic in nature. The electronic coupling is found to depend on both the superexchange interaction through the bridging oxygen atoms and the d-shell electron spin coupling within the Fe-Fe donor-acceptor pair, while the reorganization energy is essentially independent of the electron spin coupling.