Diffusion magnetic resonance imaging (dMRI) has been used to noninvasively reconstruct fiber tracts. Fiber orientation (FO) estimation is a crucial step in the reconstruction, especially in the case of crossing fibers. In FO estimation, it is important to incorporate spatial coherence of FOs to reduce the effect of noise. In this work, we propose a method of FO estimation using neighborhood information. The diffusion signal is modeled by a fixed tensor basis. The spatial coherence is enforced in weighted ℓ1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is ensured by the agreement between raw and reconstructed diffusion signals. The resulting objective function is solved using a block coordinate descent algorithm. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for qualitative and quantitative evaluation. The results demonstrate that the proposed method improves the quality of FO estimation.