With rising energy prices and concerns about environmental issues, energy-efficient driving strategies (EEDS) for high-speed trains have received a substantial amount of attention. In particular, energy-saving schemes play a huge role in reducing the energy and operating costs of trains. This article studies the EEDS of high-speed trains at a given time. A well-posed model is formulated, in which the constraints of the checkpoints, in addition to the speed limits, vehicle dynamics, and discrete control throttle, are first considered. For a given control sequence, the Karush-Kuhn-Tucker (KKT) conditions are used to obtain the necessary conditions for an EEDS. According to several key equations of the necessary conditions, the checkpoint constraints are satisfied. Some case studies are conducted based on the data of the Beijing-Shanghai high-speed line to illustrate the effectiveness of the proposed approach.