A network based on complementary consistency training, CC-Net, has been proposed for semi-supervised left atrium image segmentation. CC-Net efficiently utilizes unlabeled data from the perspective of complementary information, addressing the limited ability of existing semi-supervised segmentation algorithms to extract information from unlabeled data. The complementary symmetrical structure of CC-Net includes a main model and two auxiliary models. The complementary consistency is formed by the model-level perturbation between the main model and the auxiliary models, enforcing their consistency. The complementary information obtained by the two auxiliary models helps the main model effectively focus on ambiguous areas, while the enforced consistency between models facilitates the acquisition of low-uncertainty decision boundaries. CC-Net has been validated in two public datasets. Compared to current state-of-the-art algorithms under specific proportions of annotated data, CC-Net demonstrates the best performance in semi-supervised segmentation. Our code is publicly available at https://github.com/Cuthbert-Huang/CC-Net.