We propose a novel graph Laplacian-guided coupled tensor decomposition (gLGCTD) model for fusion of hyperspectral image (HSI) and multispectral image (MSI) for spatial and spectral resolution enhancements. The coupled Tucker decomposition is employed to capture the global interdependencies across the different modes to fully exploit the intrinsic global spatial-spectral information. To preserve local characteristics, the complementary submanifold structures embedded in high-resolution (HR)-HSI are encoded by the graph Laplacian regularizations. The global spatial-spectral information captured by the coupled Tucker decomposition and the local submanifold structures are incorporated into a unified framework. The gLGCTD fusion framework is solved by a hybrid framework between the proximal alternating optimization (PAO) and the alternating direction method of multipliers (ADMM). Experimental results on both synthetic and real data sets demonstrate that the gLGCTD fusion method is superior to state-of-the-art fusion methods with a more accurate reconstruction of the HR-HSI.