Purpose Accurate segmentation of complex tumors in lung computed tomography (CT) images is essential to improve the effectiveness and safety of lung cancer treatment. However, the characteristics of heterogeneity, blurred boundaries, and large-area adhesion to tissues with similar gray-scale features always make the segmentation of complex tumors difficult. Methods This study proposes an effective deep network for the automatic segmentation of complex lung tumors (CLT-Net). The network architecture uses an encoder-decoder model that combines long and short skip connections and a global attention unit to identify target regions using multiscale semantic information. A boundary-aware loss function integrating Tversky loss and boundary loss based on the level-set calculation is designed to improve the network's ability to perceive boundary positions of difficult-to-segment (DTS) tumors. We use a dynamic weighting strategy to balance the contributions of the two parts of the loss function. Results The proposed method was verified on a dataset consisting of 502 lung CT images containing DTS tumors. The experiments show that the Dice similarity coefficient and Hausdorff distance metric of the proposed method are improved by 13.2% and 8.5% on average, respectively, compared with state-of-the-art segmentation models. Furthermore, we selected three additional medical image datasets with different modalities to evaluate the proposed model. Compared with mainstream architectures, the Dice similarity coefficient is also improved to a certain extent, which demonstrates the effectiveness of our method for segmenting medical images. Conclusions Quantitative and qualitative results show that our method outperforms current mainstream lung tumor segmentation networks in terms of Dice similarity coefficient and Hausdorff distance. Note that the proposed method is not limited to the segmentation of complex lung tumors but also performs in different modalities of medical image segmentation.