Leveraging weak or noisy supervision for building effective machine learning models has long been an important research problem. Its importance has further increased recently due to the growing need for large-scale datasets to train deep learning models. Weak or noisy supervision could originate from multiple sources including non-expert annotators or automatic labeling based on heuristics or user interaction signals. There is an extensive amount of previous work focusing on leveraging noisy labels. Most notably, recent work has shown impressive gains by using a meta-learned instance re-weighting approach where a meta-learning framework is used to assign instance weights to noisy labels. In this paper, we extend this approach via posing the problem as a label correction problem within a meta-learning framework. We view the label correction procedure as a meta-process and propose a new meta-learning based framework termed MLC (Meta Label Correction) for learning with noisy labels. Specifically, a label correction network is adopted as a meta-model to produce corrected labels for noisy labels while the main model is trained to leverage the corrected labels. Both models are jointly trained by solving a bi-level optimization problem. We run extensive experiments with different label noise levels and types on both image recognition and text classification tasks. We compare the re-weighing and correction approaches showing that the correction framing addresses some of the limitations of re-weighting. We also show that the proposed MLC approach outperforms previous methods in both image and language tasks.