Target Off-Bock Time (TOBT) is one of the most uncertain factors in airport operation. TOBT is the pushback start time predicted by aircraft operators. Since TOBT is affected by uncertain factors such as passengers' boarding process, it is difficult to predict the accurate TOBT. The author argues that TOBT accuracy is not constant and can vary depending on the situation. This TOBT accuracy information can help to improve the airport operation. Therefore, the author proposes to predict TOBT distribution, instead of predicting TOBT at a single point. TOBT is assumed to follow Johnson-SU distribution, and the parameters of the distribution are estimated by neural network. TOBT is provided and updated by aircraft operators if required, so this TOBT update history is used to predict TOBT distribution. The benefit to predict TOBT distribution is found to assign the pushback approval time (TSAT), because the probability of each aircraft reaching the runway can be calculated at any given time. The simulation result shows the significant benefit by predicting TOBT as a distribution.