Pulmonary nodule computed tomography (CT) images have diverse details and interclass similarity. To address this problem, a dual-path cross-fusion network combining the advantages of convolutional neural network (CNN) and Transformer is constructed to classify pulmonary nodules more accurately. First, based on windows multi-head self-attention and shifted windows multi-head self-attention, a global feature block is constructed to capture the morphological features of nodules; then, a local feature block is constructed based on large kernel attention, which is used to extract internal features such as the texture and density of nodules. A feature fusion block is designed to fuse local and global features of the previous stage so that each path can collect more comprehensive discriminative information. Subsequently, Kullback-Leibler (KL) divergence is introduced to increase the distribution difference between features of different scales and optimize network performance. Finally, a decision-level fusion method is used to obtain the classification results. Experiments are conducted on the LIDC-IDRI dataset, and the network achieves a classification accuracy, recall, precision, specificity, and area under curve (AUC) of 94.16%, 93.93%, 93.03%, 92.54%, and 97.02%, respectively. Experimental results show that this method can classify benign and malignant pulmonary nodules effectively.