Diffusion tensor (DT) magnetic resonance imaging (MRI) provides the directional information of local neuronal fibers, and has been used to estimate the neuroanatomical connectivity in the cerebral white matter. Several methods for white matter tractography have been developed based on DT-MRI. However, it has been difficult to estimate the white matter tract pathways in the fiber crossing and branching region because of the ambiguity of the principal eigenvector and/or low anisotropy due to the partial volume effect. In this paper, we proposed a new method for white matter tractography, which permits fiber tract branching and passing through crossing regions. Our tractography method is based on a three-dimensional (3D) directional diffusion function (DDF), which was given by a 3D anisotropic Gaussian function defined by normalized three eigenvalues and their corresponding eigenvectors of DT. The DDF was used for generation of a 3D directional diffusion field and for determination of the connectivity between the voxels in fiber tracking. To extract the white matter tract region, DDF-based tractography (DDFT) method used the directional diffusion field instead of a threshold fractional anisotropy map, which has been used in the conventional methods, so that low anisotropy voxels in the branching and crossing regions may be included. We applied the DDFT method and two conventional tractography methods (a streamline technique and a tensorline algorithm) to DT-MRI data of five normal subjects for visualizing the pyramidal tract. Our method visualized the pathways connected to 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 in all subjects, whereas the conventional methods showed only a small portion of the pyramidal tract. The pyramidal tract pathways estimated by our method were consistent with the neuroanatomical knowledge. In conclusion, the DDFT method may be useful in assisting neuroradiologists in estimating the white matter tracts.