In recent years, enormous research has been made to improve the classification performance of single-modal remote sensing (RS) data. However, with the ever-growing availability of RS data acquired from satellite or airborne platforms, simultaneous processing and analysis of multimodal RS data pose a new challenge to researchers in the RS community. To this end, we propose a deep-learning-based new framework for multimodal RS data classification, where convolutional neural networks (CNNs) are taken as a backbone with an advanced cross-channel reconstruction module, called CCR-Net. As the name suggests, CCR-Net learns more compact fusion representations of different RS data sources by the means of the reconstruction strategy across modalities that can mutually exchange information in a more effective way. Extensive experiments conducted on two multimodal RS datasets, including hyperspectral (HS) and light detection and ranging (LiDAR) data, i.e., the Houston2013 dataset, and HS and synthetic aperture radar (SAR) data, i.e., the Berlin dataset, demonstrate the effectiveness and superiority of the proposed CCR-Net in comparison with several state-of-the-art multimodal RS data classification methods. The codes will be openly and freely available at https://github.com/danfenghong/IEEE_TGRS_CCR-Net for the sake of reproducibility.