Breast Cancer serve as one of the diseases that make a high number of deaths every year. It is the common type of all cancers and the main cause of women’s deaths worldwide. Due to the vital role of the aberrant DNA methylation during the disease development such as cancer, prediction mechanism had become essential in the recent years for early detection and diagnosis. The high-dimensionality and noisiness of the DNA methylation data may lead to the reduction of the prediction accuracy. Thus, it becomes more important in a wide range to employ robust computational tools such as feature selection and extraction methods to extract the informative features amongst thousands of them, and hence improving cancer prediction. This paper aims at predicting cancer with a hybridized feature selection and feature extraction (HFSE) techniques. The suggested approach shows a filter feature selection method called (F-score) to overcome the high-dimensionality problem of the DNA methylation data, and proposes an extraction model which employs the peaks of the mean methylation density in order to exact cancer classification and reduce training time. To evaluate the reliability of our approach, machine learning algorithms such as The naïve base and support vector machine, knn algorithms are introduced to predict cancer. The results show that, the classification accuracy improves in all cases and it also proves the reliability indirectly.