For the setting of interval censored data in which the event time is not exactly observed but known to be inside a random interval, a simple nonparametric two-sample test, based on empirical estimates of smooth functionals of the distribution function of event time, is developed to compare the distribution functions of event time for two populations. Monte Carlo simulation studies on Weibull distributions show that this test performs quite well. A real data set from an AIDS clinical trial is used to illustrate the test.