This article proposed a nonconvex variational model for pansharpening with spatial and spectral gradient difference-induced nonconvex sparsity priors (PSSGDNSP), which can fuse the panchromatic (Pan) and low-resolution (LR) multispectral (MS) images to generate the high-resolution (HR) MS image. More particularly, the proposed PSSGDNSP model exploits the spatial gradient difference-induced nonconvex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1/2}$ </tex-math></inline-formula> sparsity prior between HR MS and Pan, and the spectral gradient difference-induced nonconvex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1/2}$ </tex-math></inline-formula> sparsity prior between HR and LR MS. Consequently, our proposed PSSGDNSP model well preserves both the spatial and spectral information. In fact, our proposed band-coupled model treats the MS image like a third-order tensor so that the intrinsic band correlation of the MS image can be fully kept. Moreover, we solve our proposed PSSGDNSP model by applying the alternating direction method of multipliers (ADMM) method. Finally, the experiments fully validate the superiority and performance of our proposed PSSGDNSP method.