Automatic classification of color images of skin helps clinicians and dermatologists in examining and investigating skin melanoma. In this paper, a new deep convolutional neural network-based classification method is proposed. The proposed method consists of three main steps. First, the input color images of skin are preprocessed where the region of interest (ROI) are segmented. Second, the segmented ROI images are augmented using rotation and translation transformations. Third, different deep convolutional neural network (DCNN) architectures such as Alex-net, ResNet101, and GoogleNet are utilized. The last three layers are dropped out and replaced with new layers to be more appropriate with the task of lesion classification. The performance of the proposed method has been evaluated using three different datasets, MED-NODE, DermIS & DermQuest and ISIC 2017. The proposed DCNN have fine-tuned and trained using 85%, tested and verified using 15% of the overall datasets. The proposed method significantly improved the classification process especially with modified GoogleNet where the classification accuracy was 99.29%, 99.15%, and 98.14% for MED-NODE, DermIS & DermQuest, and ISIC 2017 respectively.