Hyperspectral image (HSI) super-resolution is a hot topic in remote sensing and computer vision. Recently, tensor analysis has been proven to be an efficient technology for HSI image processing. However, the existing tensor-based methods of HSI super-resolution are not able to capture the high-order correlations in HSI. In this article, we propose to learn a high-order coupled tensor ring (TR) representation for HSI super-resolution. The proposed method first tensorizes the HSI to be estimated into a high-order tensor in which multiscale spatial structures and the original spectral structure are represented. Then, a coupled TR representation model is proposed to fuse the low-resolution HSI (LR-HSI) and high-resolution multispectral image (HR-MSI). In the proposed model, some latent core tensors in TR of the LR-HSI and the HR-MSI are shared, and we use the relationship between the spectral core tensors to reconstruct the HSI. In addition, the graph-Laplacian regularization is introduced to the spectral core tensors to preserve the spectral information. To enhance the robustness of the proposed model, Frobenius norm regularizations are introduced to the other core tensors. Experimental results on both synthetic and real data sets show that the proposed method achieves the state-of-the-art super-resolution performance.