To get the high resolution multi-spectral (HRMS) images by the fusion of low resolution multi-spectral (LRMS) and panchromatic (PAN) images, an effectively pansharpening model with spatial Hessian non-convex sparse and spectral gradient low rank priors (PSHNSSGLR) is proposed in this paper. In particularly, from the statistical aspect of view, the spatial Hessian hyper-Laplacian non-convex sparse prior is developed to model the spatial Hessian consistency between HRMS and PAN. More importantly, it is recently the first work for pansharpening modeling with the spatial Hessian hyper-Laplacian non-convex sparse prior. Meanwhile, the spectral gradient low rank prior on HRMS is further developed for spectral feature preservation. Then, the alternating direction method of multipliers (ADMM) approach is applied for optimizing the proposed PSHNSSGLR model. Afterwards, many fusion experiments demonstrate the capability and superiority of PSHNSSGLR.