<p>In sample surveys, many estimators for the variance of non-sensitive variables have been developed by researchers. In many practical problems, the researcher may be interested in the estimation of the variance of a variable which represents some sensitive characteristics, such as illegal income, unfair means in the examination, and the amount of tax payable, etc. The rarity of studies on variance estimators of sensitive variables in the current literature leaves a big research gap for the exploration of efficient variance estimators in real-world surveys. Using the randomized response method, this study presents an efficient variance estimator of the population variance. Our findings reveal that our suggested variance estimator improves the efficiency of a recently developed variance estimator of a sensitive variable. The new estimator is based on simple random sampling using a non-sensitive auxiliary variable having correlation with the main variable. Using different values of parameters, we show improvement over the available variance estimators. Further, a simulation study has also been carried out to prove the results.</p>