Point cloud segmentation is a fundamental task in 3D. Despite recent progress on point cloud segmentation with the power of deep networks, current deep learning methods based on the clean label assumptions may fail with noisy labels. Yet, object class labels are often mislabeled in real-world point cloud datasets. In this work, we take the lead in solving this issue by proposing a novel Point Noise-Adaptive Learning (PNAL) framework. Compared to existing noise-robust methods on image tasks, our PNAL is noise-rate blind, to cope with the spatially variant noise rate problem specific to point clouds. Specifically, we propose a novel point-wise confidence selection to obtain reliable labels based on the historical predictions of each point. A novel cluster-wise label correction is proposed with a voting strategy to generate the best possible label taking the neighbor point correlations into consideration. We conduct extensive experiments to demonstrate the effectiveness of PNAL on both synthetic and real-world noisy datasets. In particular, even with $60%$ symmetric noisy labels, our proposed method produces much better results than its baseline counterpart without PNAL and is comparable to the ideal upper bound trained on a completely clean dataset. Moreover, we fully re-labeled the validation set of a popular but noisy real-world scene dataset ScanNetV2 to make it clean, for rigorous experiment and future research. Our code and data are available at url{https://shuquanye.com/PNAL_website/}.