Abstract: The estimator of expectation of interval censored data can be established by means of unbiased transformations. In this paper, we go further to study the variances of these estimators. In interval-censored Case 1 and interval-censored Case 2, when the tail of the density function of the censoring variable is thicker than that of the density function of the censored variable to some extent, the estimators with finite variance can be easily obtained.