Most existing studies on time-dependent networks have been focused on finding a minimum delay path given a departure time at the origin. There, however, frequently happens a situation where users can select any departure time in a certain time interval and want to spend as little time as possible on traveling the networks. In that case. the delay spent on traveling networks depends on not only paths but also the actual departure time at the origin. In this paper, we propose a new problem in time-dependent networks whose objective is to find an optimal departure time given possible departure time interval at the origin. From the optimal departure time, we can obtain a path with minimum delay among all paths for possible departure times at the origin. In addition, we present an algorithm for finding an optimal departure time by enumerating trees which remain shortest path tree for a certain time interval.