Diffusion tensor magnetic resonance imaging (DT-MRI) provides information about fiber direction in brain white matter and can be used for neuronal fiber pathways tracking. The purpose of our study is to develop and evaluate a novel approach for tracing anatomical fibers in vivo human brain from 3D DT-MRI tensor fields. The scheme is divided into two steps: regularization of tensor fields and fiber tracking. Firstly, 3D tensor fields are regularized to preserve directional information and discontinuous features, while removing uncorrelated noise from the data. Secondly, initiated from an operator-selected region, the anatomical fibers are bidirectionally traced based on minimizing the tracking cost (MTC) model. The model computes the possible direction of tract propagation, allowing a global trade-off among the entire tensor data, a prior knowledge of low curvature, and tracking inertia, instead of just the major eigenvector. Analysis on simulated data showed that the proposed method is less sensitive to image noise and partial volume effect than tracking using the major eigenvector, and overcomes the problem of fiber crossing successfully. Various estimated tracts obtained from human brain DT-MRI data showed that the proposed approach improves the reliability and robustness of fiber tractography. The proposed approach is effective and reproducible, which is promising for mapping the organizational patterns of white matter in the human brain as well as mapping the relationship between major fiber trajectories and the location and extent of brain lesions.