Multispectral image (MS) and panchromatic image (PAN) fusion, which is also named as multispectral pansharpening, aims to obtain MS with high spatial resolution and high spectral resolution. However, due to the usual neglect of noise and blur generated in the imaging and transmission phases of data during training, many deep learning (DL) pansharpening methods fail to perform on the dataset containing noise and blur. To tackle this problem, a variational optimization-guided two-stage network (VOGTNet) for multispectral pansharpening is proposed in this work, and the performance of variational optimization (VO)-based pansharpening methods relies on prior information and estimates of spatial-spectral degradation from the target image to other two original images. Concretely, we propose a dual-branch fusion network (DBFN) based on supervised learning and train it by using the datasets containing noise and blur to generate the prior fusion result as the prior information that can remove noise and blur in the initial stage. Subsequently, we exploit the estimated spectral response function (SRF) and point spread function (PSF) to simulate the process of spatial-spectral degradation, respectively, thereby making the prior fusion result and the adaptive recovery model (ARM) jointly perform unsupervised learning on the original dataset to restore more image details and results in the generation of the high-resolution MSs in the second stage. Experimental results indicate that the proposed VOGTNet improves pansharpening performance and shows strong robustness against noise and blur. Furthermore, the proposed VOGTNet can be extended to be a general pansharpening framework, which can improve the ability to resist noise and blur of other supervised learning-based pansharpening methods. The source code is available at https//github.com/HZC-1998/VOGTNet.