Deep convolutional neural networks (DCNNs) have contributed many breakthroughs in segmentation tasks, especially in the field of medical imaging. However, \textit{domain shift} and \textit{corrupted annotations}, which are two common problems in medical imaging, dramatically degrade the performance of DCNNs in practice. In this paper, we propose a novel robust cross-denoising framework using two peer networks to address domain shift and corrupted label problems with a peer-review strategy. Specifically, each network performs as a mentor, mutually supervised to learn from reliable samples selected by the peer network to combat with corrupted labels. In addition, a noise-tolerant loss is proposed to encourage the network to capture the key location and filter the discrepancy under various noise-contaminant labels. To further reduce the accumulated error, we introduce a class-imbalanced cross learning using most confident predictions at the class-level. Experimental results on REFUGE and Drishti-GS datasets for optic disc (OD) and optic cup (OC) segmentation demonstrate the superior performance of our proposed approach to the state-of-the-art methods.