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Accurate urban land-use mapping is a challenging task in the remote-sensing field. With the availability of diverse remote sensors, synthetic use and integration of multisource data provides an opportunity for improving urban land-use classification accuracy. Neural networks for Deep Learning have achieved very promising results in computer-vision tasks, such as image classification and object detection. However, the problem of designing an effective deep-learning model for the fusion of multisource remote-sensing data still remains. To tackle this issue, this paper proposes a modified two-branch convolutional neural network for the adaptive fusion of hyperspectral imagery (HSI) and Light Detection and Ranging (LiDAR) data. Specifically, the proposed model consists of a HSI branch and a LiDAR branch, sharing the same network structure to reduce the time cost of network design. A residual block is utilized in each branch to extract hierarchical, parallel, and multiscale features. An adaptive-feature fusion module is proposed to integrate HSI and LiDAR features in a more reasonable and natural way (based on "Squeeze-and-Excitation Networks"). Experiments indicate that the proposed two-branch network shows good performance, with an overall accuracy of almost 92%. Compared with single-source data, the introduction of multisource data improves accuracy by at least 8%. The adaptive fusion model can also increase classification accuracy by more than 3% when compared with the feature-stacking method (simple concatenation). The results demonstrate that the proposed network can effectively extract and fuse features for a better urban land-use mapping accuracy.