Skin cancer is a condition that causes the formation of abnormal cells in the skin tissue. Every year, millions of individuals experience skin cancer. Skin cancer identification in its early stages is an expensive and difficult process. Currently, deep learning models have revealed promising results in automated skin cancer classification. The goal of this study is to identify benign or malignant skin lesion using the Internation Skin Imaging Collaboration (ISIC) dataset and a concatenated model that combines two powerful Convolutional Neural Network (CNN) architectures, DenseNet and MobileNet. The ISIC dataset, which consists of a large collection of dermoscopic images, provides a valuable resource for training and evaluating skin cancer classification models. By concatenating the feature maps of DenseNet and MobileNet, the proposed model capitalizes on their individual strengths. The concatenated model is trained using a combination of techniques called transfer learning and fine-tuning, which leverage the pre-trained weights of the individual models and adapt them to the skin cancer classification task. On the test dataset, our proposed model finally achieves 93.75% accuracy, which is 4.69% higher than DenseNet, 3.13% higher than MobileNet, and 3.13% higher than the combination of ResNet50 and InceptionNetV3. The execution time of our proposed ensemble method is 49.48 min, and the execution times of MobileNet and DenseNet are 178.9 and 170.5 min, which are more than our proposed ensemble approach.