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Medical image semantic segmentation techniques can help identify tumors automatically from computed tomography (CT) scans. In this paper, we propose a Contextual and Attentional feature Fusions enhanced Convolutional Neural Network (CNN) and Transformer hybrid network (CAFCT-Net) for liver tumor segmentation. We incorporate three novel modules in the CAFCT-Net architecture: Attentional Feature Fusion (AFF), Atrous Spatial Pyramid Pooling (ASPP) of DeepLabv3, and Attention Gates (AGs) to improve contextual information related to tumor boundaries for accurate segmentation. Experimental results show that the proposed model achieves a mean Intersection over Union (IoU) of 76.54% and Dice coefficient of 84.29%, respectively, on the Liver Tumor Segmentation Benchmark (LiTS) dataset, outperforming pure CNN or Transformer methods, e.g., Attention U-Net and PVTFormer.