Title: Learning Top-k Classification with Label Ranking. Abstract: Class confusability and multi-label nature of examples inevitably arise in classification tasks with the increasing number of classes, which poses a huge challenge to classification. To mitigate this problem, top-$k$ classification is proposed, where the classifier is allowed to predict $k$ label candidates and the prediction result is considered correct as long as the ground truth label is included in the $k$ labels. However, existing top-k classification methods neglect the ranking of the ground truth label among the predicted $k$ labels, which has high application value. In this paper, we propose a novel three-stage approach to learn top-$k$ classification with label ranking. We first propose an ensemble based relabeling method and relabel the training data with $k$ labels, which is used to train the top-$k$ classifier. We then propose a novel top-$k$ classification loss function that aims to improve the ranking of the ground truth label. Finally, we have conducted extensive experiments on four text datasets and four image datasets, and the experimental results show that our method could significantly improve the performance of existing methods.