A paired comparison (PC) method is more reliable to rank or compare more than two items/ objects at the same time. It is a welldeveloped method of ordering attributes or characteristics of a given set of items.The PC model is developed using Rayleigh random variables on the basis of Stern's criteria [17]. The Rayleigh PC model is analyzed in Bayesian framework using non-informative (Jeffreys and Uniform) priors. The Bayesian inference of the developed model is compared with existing the Bradley-Terry model. The preference and predictive probabilities for current and future comparisons are calculated. The posterior probabilities of hypotheses for comparing two parameters are evaluated. The Bayesian 95% credible interval are calculated.Appropriateness of the model is also examined. Graphs of marginal posterior distributions of the parameters are drawn. The Bayesian analysis is performed using real life data sets.