Recently, Ozen et al. [6] proposed the nonparametric bootstrap method for estimating the variance of sample median and showed that this method has better efficiency for symmetric or right skewed distributions when the sample size is small. The present article proposes a new estimator for the variance of sample median. The mean squared error, variance, and bias of the new estimator is calculated and compared with those of the other estimators. The results of our simulation study show the new estimator has better efficiency for different distributions in terms of MSE.