Hypersharpening (namely, hyperspectral (HS) and multispectral (MS) image fusion) aims at enhancing the spatial resolution of HS image via an auxiliary higher resolution MS image. Currently, numerous hypersharpening methods are proposed successively, among which the unmixing-based approaches have been widely researched and demonstrated their effectiveness in the spectral fidelity aspect. However, existing unmixing-based fusion methods substantially employ mathematical techniques to solve the spectral mixture model, without taking full advantage of the collaborative spatial–spectral information that is usually helpful for abundance estimation improvement. To overcome this drawback, in this article, a novel unmixing-based HS and MS image fusion method, via a convolutional neural network (CNN), is proposed to promote spectral fidelity. The main idea of this work is to use CNN to fully explore the spatial information and the spectral information of both HS and MS images simultaneously, thereby enhancing the accuracy of estimating the abundance maps. Experiments on four simulated and real remote sensing data sets demonstrate that the proposed method is beneficial to the spectral fidelity of the fused images compared with some state-of-the-art algorithms. Meanwhile, it is also easy to implement and has a certain advantage in running time.