The spatial resolution of diffusion-weighted imaging (DWI) is limited by several physical and clinical considerations, such as practical scanning times. Interpolation methods, which are widely used to enhance resolution, often result in blurred edges. Advanced superresolution scanning acquires images with specific protocols and long acquisition times. In this paper, we propose a novel single image superresolution (SR) method which introduces high-order SVD (HOSVD) to regularize the patch-based SR framework on DWI datasets. The proposed method was implemented on an adaptive basis which ensured a more accurate reconstruction of high-resolution DWI datasets. Meanwhile, the intrinsic dimensional decreasing property of HOSVD is also beneficial for reducing the computational burden. Experimental results from both synthetic and real DWI datasets demonstrate that the proposed method enhances the details in reconstructed high-resolution DWI datasets and outperforms conventional techniques such as interpolation methods and nonlocal upsampling.