Melanoma is a type of skin cancer with a high mortality rate. The different types of skin lesions result in an inaccurate diagnosis due to their high similarity. Accurate classification of the skin lesions in their early stages enables dermatologists to treat the patients and save their lives. This paper proposes a model for a highly accurate classification of skin lesions. The proposed model utilized the transfer learning and pre-trained model with GoogleNet. The model parameters are used as initial values, and then these parameters will be modified through training. The latest well-known public challenge dataset, ISIC 2019, is used to test the ability of the proposed model to classify different kinds of skin lesions. The proposed model successfully classified the eight different classes of skin lesions, namely, melanoma, melanocytic nevus, basal cell carcinoma, actinic keratosis, benign keratosis, dermatofibroma, vascular lesion, and Squamous cell carcinoma. The achieved classification accuracy, sensitivity, specificity, and precision percentages are 94.92%, 79.8%, 97%, and 80.36%, respectively. The proposed model can detect images that do not belong to any one of the eight classes where these images are classified as unknown images.