In this paper, we consider the problem of removing clouds and recovering ground cover information from remote sensing images by proposing novel framework based on a deep unfolded and prior-aided robust principal component analysis (DUPA-RPCA) network. Clouds, together with their shadows, usually occlude ground-cover features in optical remote sensing images. This hinders the utilization of these images for a range of applications such as earth observation, land-cover classification and urban planning. We model these cloud-contaminated images as a sum of low rank and sparse elements and then unfold an iterative RPCA algorithm that has been designed for reweighted l1-minimization. As a result, the activation function in DUPA-RPCA adapts for every input at each layer of the network. Our experimental results on both Landsat and Sentinel images indicate that our method gives better accuracy and efficiency when compared with existing state of the art methods.