The current study deals with imputation of item non-response in probability proportional to size (PPS) sampling. A new imputation procedure is proposed by using the known co-variance between the study variable and the auxiliary variable in the case of quantitative sensitive study variable by considering the non-response in a randomization mechanism on the second call. An empirical study is conducted at the optimum values of kog and nog for the relative comparisons of ratio, difference, and proposed estimators, respectively, with the Hansen-Hurwitz estimator.