Currently, the recognition and classification of skin lesions faces two major challenges. First, the wide variety of skin lesions, the high similarity between different classes, and the large differences within the same class, especially pigmented skin lesions, make it difficult to identify and classify skin lesions. Second, as the limitations of the recognition algorithms of skin lesions, the recognition rates of the algorithms need to be further improved. To this end, an end-to-end structured deep Convolutional Neural Network (CNN) model was trained based on VGG19 network to achieve automated recognition and classification of pigmented skin lesions. Firstly, a data augmentation method (random crop, flip, mirror) was used for data preprocessing. Then, the pre-trained model from ImageNet was transferred to the augmented data samples to fine-tune the parameters. Meanwhile, by setting a weight of Softmax loss, the loss of minority class discriminant errors was increased to effectively alleviate the class-imbalance problem in the dataset. As a result, the recognition rate of the model was improved. Experiments were implemented on the dataset ISIC2017 using the deep learning framework PyTorch. The experimental results show that the recognition rate and sensitivity of the proposed method can reach 71.34% and 70.01%, respectively, which are 2.84 and 11.68 percentage points higher than those without the weight of Softmax loss. It is confirmed that our method is effective in the recognition and classification of skin lesions.