High speed train system has proven to be a very flexible and attractive system that can be developed under various circumstances and in different contexts and cultures. As a result, high speed trains are widely deployed around the world. Providing more reliable and higher data rate communication services for high speed trains has become one of the most urgent challenges. With vast amounts of spectrum available, the millimeter wave (mmWave) system is able to provide transmission rates of several gigabits per second for high speed trains. At the same time, mmWave communication also suffers from high attenuation, thus higher energy efficiency should be considered. This paper proposes an energy efficient power control scheme of train-ground mmWave communication for high speed trains. Considering a beam switching method for efficient beam alignment, we first establish position prediction model, the realistic direction antenna model and receive power model. And then we allocate the transmission power rationally through the power minimization algorithm while ensuring the total amount of transmission data. Based on this, this paper also develops a hybrid optimization scheme and finds the limit of total energy consumption when the number of segments goes to infinity. Through simulation with various system parameters and taking velocity estimation error into account, we demonstrate the superior performance of our schemes.