Computer-aided diagnosis (CAD) of skin diseases relies heavily on automatic skin lesion segmentation. Traditional convolutional neural networks (CNN) are limited in capturing global contextual information. To make up for this shortcoming, existing methods usually adopt Transformer replaces or stacks sequentially with CNN, but it may lead to network redundancy and loss of local details. In order to solve the above problems, a parallel skin lesion segmentation network based on CNN and Transformer was proposed. A dual-branch encoder was used to combine Transformer and CNN in parallel to improve the efficiency of global context modeling. Secondly, a fusion module was created to effectively fuse features from different levels of the two branches while reducing computational complexity. In addition, dual-path attention gate (DAG) was used to suppress noise and irrelevant information in the fused image and highlight important features. Comprehensive experiments on ISIC 2017, ISIC 2018 and PH² show that the proposed method achieves better segmentation results and has good generalization ability.