Large-scale mapping of date palm trees is vital for their consistent monitoring and sustainable management, considering their substantial commercial, environmental, and cultural value. This study presents an automatic approach for the large-scale mapping of date palm trees from very-high-spatial-resolution (VHSR) unmanned aerial vehicle (UAV) datasets, based on a deep learning approach. A U-Shape convolutional neural network (U-Net), based on a deep residual learning framework, was developed for the semantic segmentation of date palm trees. A comprehensive set of labeled data was established to enable the training and evaluation of the proposed segmentation model and increase its generalization capability. The performance of the proposed approach was compared with those of various state-of-the-art fully convolutional networks (FCNs) with different encoder architectures, including U-Net (based on VGG-16 backbone), pyramid scene parsing network, and two variants of DeepLab V3+. Experimental results showed that the proposed model outperformed other FCNs in the validation and testing datasets. The generalizability evaluation of the proposed approach on a comprehensive and complex testing dataset exhibited higher classification accuracy and showed that date palm trees could be automatically mapped from VHSR UAV images with an F-score, mean intersection over union, precision, and recall of 91%, 85%, 0.91, and 0.92, respectively. The proposed approach provides an efficient deep learning architecture for the automatic mapping of date palm trees from VHSR UAV-based images.