The early identification and treatment of various dermatological conditions depend on the detection of skin lesions. Due to advancements in computer-aided diagnosis and machine learning approaches, learning-based skin lesion analysis methods have attracted much interest recently. Employing the concept of transfer learning, this research proposes a deep convolutional neural network (CNN)-based multistage and multiclass framework to categorize seven types of skin lesions. In the first stage, a CNN model was developed to classify skin lesion images into two classes, namely benign and malignant. In the second stage, the model was then used with the transfer learning concept to further categorize benign lesions into five subcategories (melanocytic nevus, actinic keratosis, benign keratosis, dermatofibroma, and vascular) and malignant lesions into two subcategories (melanoma and basal cell carcinoma). The frozen weights of the CNN developed–trained with correlated images benefited the transfer learning using the same type of images for the subclassification of benign and malignant classes. The proposed multistage and multiclass technique improved the classification accuracy of the online ISIC2018 skin lesion dataset by up to 93.4% for benign and malignant class identification. Furthermore, a high accuracy of 96.2% was achieved for subclassification of both classes. Sensitivity, specificity, precision, and F1-score metrics further validated the effectiveness of the proposed multistage and multiclass framework. Compared to existing CNN models described in the literature, the proposed approach took less time to train and had a higher classification rate.