Computer Aided Diagnosis (CAD) is used to assist radiologist in classifying various type of breast cancers. It already proved its success not only in reducing human error in reading the mammograms but also shows better and reliable classification into benign and malignant abnormalities. This paper will report and attempt on using Radial Basis Function Neural Network (RBFNN) for mammograms classification based on Gray-level Co-occurrence Matrix (GLCM) texture based features. In this study, normal and abnormal breast image used as the standard input are taken from Mammographic Image Analysis Society (MIAS) digital mammogram database. The computational experiments show that RBFNN is better than Back-propagation Neural Network (BPNN) in performing breast cancer classification. For normal and abnormal classification, the result shows that RBFNN's accuracy is 93.98%, which is 14% higher than BPNN, while the accuracy of benign and malignant classification is 94.29% which is 2% higher than BPNN.