Lung cancer is one of the malignant tumors with high morbidity and mortality, and lung nodules are the early stages of lung cancer. The symptoms of pulmonary nodules are not obvious in the clinic, and the optimal treatment time is missed due to the missed diagnosis in the clinic. A parallel U-Net network called APU-Net is proposed. Firstly, two parallel U-Net networks are used to extract the features of different modalities. Among them, the subnetwork UNet_B extracts the CT image features, and the subnetwork UNet_A consists of two encoders to extract the PET/CT and PET image features. Secondly, multimodal feature extraction blocks are used to extract features for PET/CT and PET images in UNet_B network. Thirdly, a hybrid attention mechanism is added to the encoding paths of the UNet_A and UNet_B. Finally, a multiscale feature aggregation block is used for extracting feature maps of different scales of decoding path. On the lung tumor (18)FDGPET/CT multimodal medical images dataset, experiments' results show that the DSC, Recall, VOE, and RVD coefficients of APU-Net are 96.86%, 97.53%, 3.18%, and 3.29%, respectively. APU-Net can improve the segmentation accuracy of the adhesion between the lesion of complex shape and the normal tissue. This has positive significance for computer-aided diagnosis.