Receiver Operating Characteristic (ROC) Curve is a widely used classification technique in Medical Diagnosis which classifies the healthy and diseased individuals on the basis of optimal cut off value of the biomarker. In this article, we have proposed Constant Shape Weibull Mixture ROC (CSWMROC) model. The properties of CSWMROC Curve are discussed and expressions for AUC, its variance and confidence interval are derived. The estimates of AUC of CSWMROC curve are obtained using Method of Moments (MOM). Numerical example is considered to support the proposed theory.