The objective of the pansharpening task is to integrate multispectral (MS) images with low spatial resolution (LR) and to integrate panchromatic (PAN) images with high spatial resolution (HR) to generate HRMS images. Recently, deep learning-based pansharpening methods have been widely studied. However, traditional deep learning methods lack transparency while deep unrolling methods have limited performance when using one implicit prior for HRMS images. To address this issue, we incorporate one implicit prior with a semi-implicit prior and propose a double prior deep unrolling network (DPDU-Net) for pansharpening. Specifically, we first formulate the objective function based on observation models of PAN and LRMS images and two priors of an HRMS image. In addition to the implicit prior in the image domain, we enforce the sparsity of the HRMS image in a certain multi-scale implicit space; thereby, the feature map can obtain better sparse representation ability. We optimize the proposed objective function via alternating iteration. Then, the iterative process is unrolled into an elaborate network, with each iteration corresponding to a stage of the network. We conduct both reduced-resolution and full-resolution experiments on two satellite datasets. Both visual comparisons and metric-based evaluations consistently demonstrate the superiority of the proposed DPDU-Net.