In this paper,we propose a new non-randomized response (NRR) model,called a variant of the parallel model.A survey design and corresponding statistical inferences including likelihood-based methods,Bayesian methods and bootstrap methods are provided.Theoretical and numerical comparisons showed that the proposed variant of the parallel model over-performs two existing NRR crosswise and triangular models for most of the possible parameter ranges.A real dateset from a survey on ‘sexual practices in San Francisco,Las Vegas and Portland is used to illustrate the proposed methods.