Hyperspectral imagery (HSI) contains rich spectral information, which is beneficial to many tasks. However, acquiring HSI is difficult because of the limitations of current imaging technology. As an alternative method, spectral super-resolution aims at reconstructing HSI from its corresponding RGB image. Recently, deep learning has shown its power to this task, but most of the used networks are transferred from other domains, such as spatial super-resolution. In this paper, we attempt to design a spectral super-resolution network by taking advantage of two intrinsic properties of HSI. The first one is the spectral correlation. Based on this property, a decomposition subnetwork is designed to reconstruct HSI. The other one is the projection property, i.e., RGB image can be regarded as a three-dimensional projection of HSI. Inspired from it, a self-supervised subnetwork is constructed as a constraint to the decomposition subnetwork. These two subnetworks constitute our end-to-end super-resolution network. In order to test the effectiveness of it, we conduct experiments on three widely used HSI datasets (i.e., CAVE, NUS, and NTIRE2018). Experimental results show that our proposed network can achieve competitive reconstruction performance in comparison with several state-of-the-art networks.