The recent success of deep neural networks is powered in part by large-scale well-labeled training data. However, it is a daunting task to laboriously annotate an ImageNet-like dateset. On the contrary, it is fairly convenient, fast, and cheap to collect training images from the Web along with their noisy labels. This signifies the need of alternative approaches to training deep neural networks using such noisy labels. Existing methods tackling this problem either try to identify and correct the wrong labels or reweigh the data terms in the loss function according to the inferred noisy rates. Both strategies inevitably incur errors for some of the data points. In this paper, we contend that it is actually better to ignore the labels of some of the data points than to keep them if the labels are incorrect, especially when the noisy rate is high. After all, the wrong labels could mislead a neural network to a bad local optimum. We suggest a two-stage framework for the learning from noisy labels. In the first stage, we identify a small portion of images from the noisy training set of which the labels are correct with a high probability. The noisy labels of the other images are ignored. In the second stage, we train a deep neural network in a semi-supervised manner. This framework effectively takes advantage of the whole training set and yet only a portion of its labels that are most likely correct. Experiments on three datasets verify the effectiveness of our approach especially when the noisy rate is high.