Currently, convolutional neural networks (CNNs) have made remarkable achievements in skin lesion classification because of their end-to-end feature representation abilities. However, precise skin lesion classification is still challenging because of the following three issues: (1) insufficient training samples, (2) inter-class similarities and intra-class variations, and (3) lack of the ability to focus on discriminative skin lesion parts. To address these issues, we propose a deep metric attention learning CNN (DeMAL-CNN) for skin lesion classification. In DeMAL-CNN, a triplet-based network (TPN) is first designed based on deep metric learning, which consists of three weight-shared embedding extraction networks. TPN adopts a triplet of samples as input and uses the triplet loss to optimize the embeddings, which can not only increase the number of training samples, but also learn the embeddings robust to inter-class similarities and intra-class variations. In addition, a mixed attention mechanism considering both the spatial-wise and channel-wise attention information is designed and integrated into the construction of each embedding extraction network, which can further strengthen the skin lesion localization ability of DeMAL-CNN. After extracting the embeddings, three weight-shared classification layers are used to generate the final predictions. In the training procedure, we combine the triplet loss with the classification loss as a hybrid loss to train DeMAL-CNN. We compare DeMAL-CNN with the baseline method, attention methods, advanced challenge methods, and state-of-the-art skin lesion classification methods on the ISIC 2016 and ISIC 2017 datasets, and test its generalization ability on the PH2 dataset. The results demonstrate its effectiveness.