With the widespread success of deep learning in biomedical image segmentation, domain shift becomes a critical and challenging problem, as the gap between two domains can severely affect model performance when deployed to unseen data with heterogeneous features. To alleviate this problem, we present a novel unsupervised domain adaptation network, for generalizing models learned from the labeled source domain to the unlabeled target domain for cross-modality biomedical image segmentation. Specifically, our approach consists of two key modules, a conditional domain discriminator~(CDD) and a category-centric prototype aligner~(CCPA). The CDD, extended from conditional domain adversarial networks in classifier tasks, is effective and robust in handling complex cross-modality biomedical images. The CCPA, improved from the graph-induced prototype alignment mechanism in cross-domain object detection, can exploit precise instance-level features through an elaborate prototype representation. In addition, it can address the negative effect of class imbalance via entropy-based loss. Extensive experiments on a public benchmark for the cardiac substructure segmentation task demonstrate that our method significantly improves performance on the target domain.