Early detection of skin cancer through improved techniques and innovative technologies has the greatest potential for significantly reducing both morbidity and mortality associated with this disease. In this paper, an effective framework of a CAD (Computer-Aided Diagnosis) system for melanoma skin cancer is developed mainly by application of an SVM (Support Vector Machine) model on an optimized set of HOG (Histogram of Oriented Gradient) based descriptors of skin lesions. Experimental results obtained by applying the presented methodology on a large, publicly accessible dataset of dermoscopy images demonstrate that the proposed framework is a strong contender for the state-of-the-art alternatives by achieving high levels of sensitivity, specificity, and accuracy (98.21%, 96.43% and 97.32%, respectively), without sacrificing computational soundness.