Skin cancer is one of most deadly diseases in humans. According to the high similarity between melanoma and nevus lesions, physicians take much more time to investigate these lesions. The automated classification of skin lesions will save effort, time and human life. The purpose of this paper is to present an automatic skin lesions classification system with higher classification rate using the theory of transfer learning and the pre-trained deep neural network. The transfer learning has been applied to the Alex-net in different ways, including fine-tuning the weights of the architecture, replacing the classification layer with a softmax layer that works with two or three kinds of skin lesions, and augmenting dataset by fixed and random rotation angles. The new softmax layer has the ability to classify the segmented color image lesions into melanoma and nevus or into melanoma, seborrheic keratosis, and nevus. The three well-known datasets, MED-NODE, Derm (IS & Quest) and ISIC, are used in testing and verifying the proposed method. The proposed DCNN weights have been fine-tuned using the training and testing dataset from ISIC in addition to 10-fold cross validation for MED-NODE and DermIS-DermQuest. The accuracy, sensitivity, specificity, and precision measures are used to evaluate the performance of the proposed method and the existing methods. For the datasets, MED-NODE, Derm (IS & Quest) and ISIC, the proposed method has achieved accuracy percentages of 96.86%, 97.70%, and 95.91% respectively. The performance of the proposed method has outperformed the performance of the existing classification methods of skin cancer.