Deep neural networks are susceptible to overfitting with noisy labels. Existing meta-learning-based methods for learning with noisy labels require additional clean validation data, resulting in high annotation costs and limiting their general applicability. Moreover, these methods only use local gradient information to approximately optimize the model parameters. In this paper, we propose a novel meta label corrector to address the above two issues. Our method is based on two core points: monitoring training dynamics through the meta-entropy value to construct a proxy clean validation dataset, and precise parameter optimization through a new combined bi-level optimization mechanism. Compared with state-of-the-art noisy label learning methods, comprehensive experiments confirm the superiority of our method in both image recognition and text classification with different label noise types and ratios.