Melanoma is deadly skin cancer. There is a high similarity between different kinds of skin lesions, which lead to incorrect classification. Accurate classification of a skin lesion in its early stages saves human life. In this paper, a highly accurate method proposed for the skin lesion classification process. The proposed method utilized transfer learning with pre-trained AlexNet. The parameters of the original model used as initial values, where we randomly initialize the weights of the last three replaced layers. The proposed method was tested using the most recent public dataset, ISIC 2018. Based on the obtained results, we could say that the proposed method achieved a great success where it accurately classifies the skin lesions into seven classes. These classes are melanoma, melanocytic nevus, basal cell carcinoma, actinic keratosis, benign keratosis, dermatofibroma, and vascular lesion. The achieved percentages are 98.70%, 95.60%, 99.27%, and 95.06% for accuracy, sensitivity, specificity, and precision, respectively.