PURPOSE Noise in magnetic resonance imaging (MRI) data is widely recognized to be harmful to image processing and subsequent quantitative analysis. To ameliorate the effects of image noise, the authors present a structure-tensor based nonlocal mean (NLM) denoising technique that can effectively reduce noise in MRI data and improve tissue characterization. METHODS The proposed 3D NLM algorithm uses a structure tensor to characterize information around tissue boundaries. The similarity weight of a pixel (or patch), which determines its contribution to the denoising process, is determined by the intensity and structure tensor simultaneously. Meanwhile, similarity of structure tensors is computed using an affine-invariant Riemannian metrics, which compares tensor properties more comprehensively and avoids orientation inaccuracy of structure subsequently. The proposed method is further extended for denoising high dimensional MRI data such as diffusion weighted MRI. It is also extended to handle Rician noise corruption so that denoising effects are further enhanced. RESULTS The proposed method was implemented in both simulated datasets and multiply modalities of real 3D MRI datasets. Comparisons with related state-of-the-art algorithms demonstrated that this method improves denoising performance qualitatively and quantitatively. CONCLUSIONS In this paper, high order structure information of 3D MRI was characterized by 3D structure tensor and compared for NLM denoising in a Riemannian space. Experiments with simulated and real human MRI data demonstrate a great potential of the proposed technique for routine clinical use.