Skin cancer is the most common type of cancer that affects humans and is usually diagnosed by initial clinical screening, which is followed by dermoscopic analysis. Automated classification of skin lesions is still a challenging task because of the high visual similarity between melanoma and benign lesions. This paper proposes a new residual deep convolutional neural network (RDCNN) for skin lesions diagnosis. The proposed neural network is trained and tested using six well-known skin cancer datasets, PH2, DermIS and Quest, MED-NODE, ISIC2016, ISIC2017, and ISIC2018. Three different experiments are carried out to measure the performance of the proposed RDCNN. In the first experiment, the proposed RDCNN is trained and tested using the original dataset images without any pre-processing or segmentation. In the second experiment, the proposed RDCNN is tested using segmented images. Finally, the utilized trained model in the second experiment is saved and reused in the third experiment as a pre-trained model. Then, it is trained again using a different dataset. The proposed RDCNN shows significant high performance and outperforms the existing deep convolutional networks.