Since label noise can hurt the performance of supervised learning (SL), how to train a good classifier to deal with label noise is an emerging and meaningful topic in machine learning field. Although many related methods have been proposed and achieved promising performance, they have the following drawbacks:(1) They can lead to data waste and even performance degradation if the mislabeled instances are removed; and (2) the negative effect of the extremely mislabeled instances cannot be completely eliminated. To address these problems, we propose a novel method based on the capped ℓ 1 norm and a graph-based regularizer to deal with label noise. In the proposed algorithm, we utilize the capped ℓ 1 norm instead of the ℓ 1 norm. The used norm can inherit the advantage of the ℓ 1 norm, which is robust to label noise to some extent. Moreover, the capped ℓ 1 norm can adaptively find extremely mislabeled instances and eliminate the corresponding negative influence. Additionally, the proposed algorithm makes full use of the mislabeled instances under the graph-based framework. It can avoid wasting collected instance information. The solution of our algorithm can be achieved through an iterative optimization approach. We report the experimental results on several UCI datasets that include both binary and multi-class problems. The results verified the effectiveness of the proposed algorithm in comparison to existing state-of-the-art classification methods.