In radiotherapy planning, manual contouring is labor-intensive and time-consuming. Accurate and robust automated segmentation models improve the efficiency and treatment outcome. We aim to develop a novel hybrid deep learning approach, combining convolutional neural networks (CNNs) and the self-attention mechanism, for rapid and accurate multi-organ segmentation on head and neck computed tomography (CT) images. Head and neck CT images with manual contours of 115 patients were retrospectively collected and used. We set the training/validation/testing ratio to 81/9/25 and used the 10-fold cross-validation strategy to select the best model parameters. The proposed hybrid model segmented ten organs-at-risk (OARs) altogether for each case. The performance of the model was evaluated by three metrics, i.e., the Dice Similarity Coefficient (DSC), Hausdorff distance 95% (HD95), and mean surface distance (MSD). We also tested the performance of the model on the Head and Neck 2015 challenge dataset and compared it against several state-of-the-art automated segmentation algorithms. The proposed method generated contours that closely resemble the ground truth for ten OARs. Our results of the new Weaving Attention U-net demonstrate superior or similar performance on the segmentation of head and neck CT images.