Automatic segmentation of pulmonary nodules on computed tomography (CT) images can aid in the early diagnosis and treatment of lung cancer. However, this task is challenging due to the heterogeneity among different types of pulmonary nodules and the similarity in grayscale values between the nodules and surrounding lung tissue. To effectively improve the pulmonary nodule segmentation, we propose a new boundary-aware dual-branch neural network. In the first phase, our edge guidance module integrates multi-level encoder outputs to capture key boundary information and suppress non-target edges. The second phase uses a feature fusion module to dynamically combine high-level semantic information and boundary features. Finally, a dynamic convolutional attention module refines skip connections through dynamic spatial attention, identifying key spatial regions and generating attention maps to highlight the most distinctive and representative features. Extensive experiments on the publicly available LIDC-IDRI lung dataset demonstrate that our method significantly improves the segmentation performance of pulmonary nodules in CT images compared to existing segmentation techniques.