High resolution diffusion tensor imaging and tractography of ex vivo brain specimens has the potential to reveal detailed fibre architecture not visible on in vivo images. Previous ex vivo diffusion imaging experiments have focused on animal brains or small sections of human tissue since the unfavourable properties of fixed tissue (including short T(2) and low diffusion rates) demand the use of very powerful gradient coils that are too small to accommodate a whole, human brain. This study proposes the use of diffusion-weighted steady-state free precession (DW-SSFP) as a method of extending the benefits of ex vivo DTI and tractography to whole, human, fixed brains on a clinical 3 T scanner. DW-SSFP is a highly efficient pulse sequence; however, its complicated signal dependence precludes the use of standard diffusion tensor analysis and tractography. In this study, a method is presented for modelling anisotropy in the context of DW-SSFP. Markov Chain Monte Carlo sampling is used to estimate the posterior distributions of model parameters and it is shown that it is possible to estimate a tight distribution on the principal axis of diffusion at each voxel using DW-SSFP. Voxel-wise estimates are used to perform tractography in a whole, fixed human brain. A direct comparison between 3D diffusion-weighted spin echo EPI and 3D DW-SSFP-EPI reveals that the orientation of the principal diffusion axis can be inferred on with a higher degree of certainty using a 3D DW-SSFP-EPI even with a 68% shorter acquisition time.