Nowadays people are suffering from different diseases caused by pollution, stress and bad nutrition. Doctors and biologists have to diagnose, detect and find corresponding treatment. Even most of the diseases are treated; some type of disease like cancer needs early detection and preventive treatment. In this paper, we provide a solution for early cancer disease detection. Our method consists of analyzing miRNAs expression for many cancer types leveraging a novel machine learning approach grounded in the Support Vector Machine framework: Twin-Support Vector Machine (twinSVM). The predicted area under the curve (AUC) yielded up to 92.44% over a cancer disease-miRNA association dataset with the polynomial kernel. The accuracy, precision and recall were 94.73%, 98.16%, and 96%, respectively. With our model, the achieved AUC outperformed those obtained by methods existing in the state of the art. Further, a comparison with SVM showed that TWSVM outperformed SVM in terms of accuracy, and AUC. Indeed, SVM with linear kernel reached 93.55% as accuracy and 91.84% as AUC value.