Optic disc and cup segmentation play a crucial role in automating the screening and diagnosis of optic glaucoma. While data-driven convolutional neural networks (CNNs) show promise in this area, the inherent ambiguity of segmenting object and background boundaries in the task of optic disc and cup segmentation leads to noisy annotations that impact model performance. To address this, we propose an innovative label-denoising method of Multiple Pseudo-labels Noise-aware Network (MPNN) for accurate optic disc and cup segmentation. Specifically, the Multiple Pseudo-labels Generation and Guided Denoising (MPGGD) module generates pseudo-labels by multiple different initialization networks trained on true labels, and the pixel-level consensus information extracted from these pseudo-labels guides to differentiate clean pixels from noisy pixels. The training framework of the MPNN is constructed by a teacher-student architecture to learn segmentation from clean pixels and noisy pixels. Particularly, such a framework adeptly leverages (i) reliable and fundamental insights from clean pixels and (ii) the supplementary knowledge within noisy pixels via multiple perturbation-based unsupervised consistency. Compared to other label-denoising methods, comprehensive experimental results on the RIGA dataset demonstrate our method's excellent performance and significant denoising ability.