Improving the spatial resolution of a hyperspectral image (HSI) is of great significance in the remotely sensed field. By fusing a high-spatial-resolution multispectral image (MSI) with an HSI collected from the same scene, hyperspectral and multispectral (HS–MS) fusion has been an emerging technique to address the issue. Extracting complex spatial information from MSIs while maintaining abundant spectral information of HSIs is essential to generate the fused high-spatial-resolution HSI (HS ² I). A common way is to learn low-rank/sparse representations from HSI and MSI, then reconstruct the fused HS ² I based on tensor/matrix decomposition or unmixing paradigms, which ignore the intrinsic geometry proximity inherited by the low-rank property of the fused HS ² I. This study proposes to estimate the high-resolution HS ² I via low-rank tensor approximation with geometry proximity as side information learned from MSI and HSI by defined graph signals, which we name GLRTA. Row graph and column graph are defined on the horizontal slice and lateral slice of MSI tensor respectively, while spectral band graph is defined on a frontal slice of HSI tensor . Experimental results demonstrate that the proposed GLRTA can effectively improve the reconstruction results compared to other competitive works.