To investigate the mechanisms responsible for electrical conduction and deduce the relation between grain size and conductivity, the electrical conductivity of synthetic polycrystalline forsterite, with grain sizes between 1.1 ¿ 0.4 and 4.7 ¿ 2.4 ¿m, was measured at temperatures up to 1470¿C and at 0.1 MPa pressure. The complex impedance plots display one clear arc, indicating a single dominant conduction mechanism. Bulk conductivity is inversely proportional to the grain size of the different samples. This relation suggests that the electrical conductivity of the samples is controlled by grain boundary diffusion of the charge carriers. The apparent activation energy (Q) for diffusion of the charge carriers between 1180¿ and 1470¿C lies between 315 ¿ 39 and 323 ¿ 15 kJ/mol. This resembles previous data on grain boundary diffusion of Mg in forsterite. A geometrical model of less-conducting cubic grains and more-conducting grain boundaries agrees well with the experimental data. This model is applied to predict the conductivity contrast between fine-grained shear zones and less-deformed regions in the lithosphere. Upper mantle shear zones are predicted to have 1.5--2 orders of magnitude higher conductivity than less-deformed regions in the lithosphere. This means grain boundary transport probably has an important role in the existence of anomalously high conductivity zones in the upper mantle and that fine-grained shear zones might be detected using magnetotelluric methods.