Sensitive topics or highly personal questions are often faced in medical psychological and socio-economic survey. Warner's pioneering randomized response (RR) device, as a method for reducing evasive answer bias while estimating the proportion of people in a community bearing a sensitive attribute, has been studied extensively over the last four decades. This paper proposes a new model (named the logistic model) for survey sampling with sensitive characteristics, and provides the suitable estimators for estimating an unknown proportion of people bearing a sensitive characteristic in a given community. That is a development for some existing research results concerning the randomized response theory. A numerical study comparing the performance of the proposed procedure and Warner's (1965)[10]procedure is reported.