Electroencephalogram (EEG) source analysis is typically done using head models with isotropic tissue conductivities. This ignores the fact that some tissues are known to be highly anisotropic. In this study, we investigate the effect that tissue anisotropy has on the EEG inverse problem. EEG electrode voltages are simulated using the forward problem solution for an anisotropic head model, while the inverse problem is solved for an isotropic head model. The error associated with neglecting anisotropy is quantified with the source localization error. A realistic head model is generated from magnetic resonance images and anisotropic conductivity values are estimated from diffusion tensor images. All calculations are done with the finite volume method on a cubic grid with 1 mm resolution. We determine that neglecting to account for anisotropy can cause considerable source localization errors, indicating that the anisotropic conductivities should not be ignored in EEG source analysis.