We propose a reconstructed diffusion gradient (RDG) method for spatial normalization of diffusion tensor imaging (DTI) data that warps the raw imaging data and then estimates the associated gradient direction for reconstruction of normalized DTI in the template space. The RDG method adopts the backward mapping strategy for DTI normalization, with a specially designed approach to reconstruct a specific gradient direction in combination with the local deformation force. The method provides a voxel-based strategy to make the gradient direction align with the raw diffusion weighted imaging (DWI) volumes, ensuring correct estimation of the tensors in the warped space and thereby retaining the orientation information of the underlying structure. Compared with the existing tensor reorientation methods, experiments using both simulated and human data demonstrated that the RDG method provided more accurate tensor information. Our method can properly estimate the gradient direction in the template space that has been changed due to image transformation, and subsequently use the warped imaging data to directly reconstruct the warped tensor field in the template space, achieving the same goal as directly warping the tensor image. Moreover, the RDG method also can be used to spatially normalize data using the Q-ball imaging (QBI) model.