The breast cancer censored data of 254 patients was considered for the survival rate estimates. The data [12, 18] was treated at the chemotherapy department, Bradford Royal Infirmary for ten years. Here in this paper Gamma probabilitydistribution model is used to obtain the survival rates of the patients (see [2], [6], [13]). Maximum likelihood method has been used through unconstrained BFGS optimization method [5, 8, 9, 10] (BFGS-Broyden Fletcher-Goldfarb and Shanno Method) to find the parameter estimates and variance-covariance matrix for the Gamma distribution model. Finally the survivor rate estimates for the parametric Gamma probability model has been compared with the non-parametric (Kaplan-Meier-[15]) method.