Lesion segmentation is a fundamental step for the diagnosis of acute ischemic stroke (AIS). Non-contrast CT (NCCT) is still a mainstream imaging modality for AIS lesion measurement. However, AIS lesion segmentation on NCCT is challenging due to low contrast, noise and artifacts. To achieve accurate AIS lesion segmentation on NCCT, this study proposes a hybrid convolutional neural network (CNN) and Transformer network with circular feature interaction and bilateral difference learning. It consists of parallel CNN and Transformer encoders, a circular feature interaction module, and a shared CNN decoder with a bilateral difference learning module. A new Transformer block is particularly designed to solve the weak inductive bias problem of the traditional Transformer. To effectively combine features from CNN and Transformer encoders, we first design a multi-level feature aggregation module to combine multi-scale features in each encoder and then propose a novel feature interaction module containing circular CNN-to-Transformer and Transformer-to-CNN interaction blocks. Besides, a bilateral difference learning module is proposed at the bottom level of the decoder to learn the different information between the ischemic and contralateral sides of the brain. The proposed method is evaluated on three AIS datasets: the public AISD, a private dataset and an external dataset. Experimental results show that the proposed method achieves Dices of 61.39% and 46.74% on the AISD and the private dataset, respectively, outperforming 17 state-of-the-art segmentation methods. Besides, volumetric analysis on segmented lesions and external validation results imply that the proposed method is potential to provide support information for AIS diagnosis.