Reconstruction of accurate cortical surfaces with minimal topological errors (i.e., handles and holes) from infant brain MR images is important in early brain development studies. However, infant brain MR images usually exhibit extremely low tissue contrast (especially from 3 to 9 months of age) and dynamic imaging appearance patterns. Thus, it is inevitable to have large amounts of topological errors in the infant brain tissue segmentation results, thus leading to inaccurate surface reconstruction. To address these issues, inspired by recent advances in deep learning methods, we propose an anatomically constrained U-Net method for topological correction of infant cortical surfaces. Specifically, in our method, we first extract candidate voxels with potential topological errors, by leveraging a topology-preserving level set method. Then, we propose a U-Net with anatomical constraints to correct those located candidate voxels. Due to the fact that infant cortical surfaces often contain large handles or holes, it is difficult to completely correct all errors using one-shot correction. Therefore, we further gather these two steps into an iterative framework to correct large topological errors gradually. To our knowledge, this is the first work introducing deep learning for infant cortical topological correction. We compare our method with the state-of-the-art method on infant cortical topology and show the superior performance of our method.