Interval censored failure time data often occurs in an observational study where a subject is followed periodically. Instead of observing an exact failure time, two inspection times that include it are made available. Several methods have been suggested to analyze interval censored failure time data (Sun, 2006). In this article, we are concerned with a binary time-varying covariate whose changing time is interval censored. A modified estimating equation is proposed by extending the approach suggested in the presence of a missing covariate. Based on simulation results, the proposed method shows a better performance than other simple imputation methods. ACTG 181 dataset were analyzed as a real example.