It is generally known that pan-sharpening is fundamentally a PAN-guided multispectral (MS) image super-resolution problem that involves learning the nonlinear mapping from low-resolution (LR) to high-resolution (HR) MS images. Since an infinite number of HR-MS images can be downsampled to produce the same corresponding LR-MS image, learning the mapping from LR-MS to HR-MS image is typically ill-posed and the space of the possible pan-sharpening functions can be extremely large, making it difficult to estimate the optimal mapping solution. To address the above issue, we propose a closed-loop scheme that learns the two opposite mapping including the pan-sharpening and its corresponding degradation process simultaneously to regularize the solution space in a single pipeline. More specifically, an invertible neural network (INN) is introduced to perform a bidirectional closed-loop: the forward operation for LR-MS pan-sharpening and the backward operation for learning the corresponding HR-MS image degradation process. In addition, given the vital importance of high-frequency textures for the Pan-sharpened MS images, we further strengthen the INN by designing a specified multiscale high-frequency texture extraction module. Extensive experimental results demonstrate that the proposed algorithm performs favorably against state-of-the-art methods qualitatively and quantitatively with fewer parameters. Ablation studies also verify the effectiveness of the closed-loop mechanism in pan-sharpening. The source code is made publicly available at https://github.com/manman1995/pan-sharpening-Team-zhouman/.