One of the most important applications of diffusion tensor image (DTI) is the in-vivo investigation of brain white-matter connectivity. However, DTI has difficulties on the reconstruction of axonal fibers. The data that is used to reconstruct the fibers is affected by partial volume effect, particularly at the border between gray and white matter, and the typical voxel size used in the acquisition of the MR images is larger than the characteristic size of the axonal fiber. The proposed vector criterion tracking method uses selective eigenvector interpolation for fiber tracking. As a result, the method produces faster and more stable trajectories with reducing memory consumption, compared to other current methods.