Finding a train operation which minimizes energy consumption for leading the train from one station to the next at the specified instant and stopping it there is dealt with in this paper. Since speed limit is observed strictly in the train operation, the problem should be considered as a bounded state variable problem. It is true that solving a bounded state variable problem is universally considered extremely troublesome, but the author has recently developed a very simple and clear method. The method is applied to this problem and the optimal control law has really been obtained straightforward and definitely. The author's is again confirmed to be very convenient to solve a bounded state variable problem. The research is believed to be the first scientific research on the economization of train operation.