Cervical cancer is a cancer that associated with infection with Human Papillomavirus (HPV). It occurs when the cells grow abnormally on the lowest portion of the woman's uterus. Most precancerous cervical cancer cases are on 20s or 30s women, but most cases diagnosed on 50s women. Cervical cancer has slow progression, it is one of the most preventable cancer and can be prevented by effective treatment. So, timely detection is important to know what effective treatment we can use. Machine learning techniques are being largely used to classify cervical cancer because of its precision and its capability to diagnose efficiently. In this paper, to identify the classification of cervical cancer, we have proposed a Gauss Newton representation-based algorithm (GNRBA) methods. Sparse representation is used with training sample selection, and Euclidean distance measure is used in the subset selection. The proposed method is less complexity, as compared to traditional representation method, more effective and easier to implement. This GNBRA method is examined on the cervical cancer database from Kaggle dataset repository. We used Stratified Shuffle Split to split the data. The experimental results show that the proposed GNBRA method give the 93 % accuracy. So, GNBRA method could be an ideal alternative for helping the clinical experts to classify cervical cancer.