In this paper we propose a logistic regression method to estimate the survival function and the median survival time in interval-censored data. The proposed method is motivated by the data augmentation technique with no sacrifice in augmenting data. In addition, we develop a cross validation criterion to determine the size of data augmentation. We compare the proposed estimator with other existing methods such as the parametric method, the single point imputation method, and the nonparametric maximum likelihood estimator through extensive numerical studies to show that the proposed estimator performs better than others in the sense of the mean squared error. An illustrative example based on a real data set is given.