Diffusion tensor magnetic resonance imaging (DT-MRI) provides directional information of diffusion of water molecules which can be utilized to estimate the connectivity of white matter tract pathways in the human brain. Many tractography methods have been developed for estimating the white matter tract pathways in the human brain using only the major eigenvector from DT-MRI. However, most of these conventional methods fail to estimate the white matter tract pathways in the fiber crossing and branching region due to the ambiguity of the major eigenvector of DT. In this study, we have developed a new tractography method for estimating the entire white matter tract pathways. Our tractography method determined the fiber tract direction based on the degree of the connectivity defined by a three-dimensional (3-D) directional diffusion function (DDF), which was based on a Gaussian model of the diffusion property. To extract the white matter tract regions, we introduced a 3-D directional diffusion field, which was generated by the DDF, into the DT-MRI voxel space. The DDF-based tractography estimated the local tract direction based on overlap of the DDFs instead of the major eigenvector, which has been used in conventional methods, and reconstructed tract branching by using a one-to-many voxel connectivity. We applied our method to DT-MRI data of 5 normal subjects and 16 patients with a brain tumor, and estimated the pyramidal tract. The results were compared with those by a conventional streamline technique. In all tractograms, our method better visualized the pathways connected with a large portion of the primary motor cortex, including foot, hand and face motor areas, passing through the crossing regions with other white matter tracts. The estimated pathways were consistent with the neuroanatomical knowledge.