Aiming at the system errors caused by uncertain running resistances, model errors and other factors during the high-speed train operation, a new adaptive error compensation control scheme based on characteristic model is proposed to realize the asymptotic tracking of a given target speed curve. Firstly, the characteristic model of high-speed train with system errors is derived based on the characteristic modeling method and the parameter identification by the dynamic analysis of high-speed train. Secondly, an adaptive error compensation controller for high-speed train based on the characteristic model is designed by employing the ability of the extended state observer for the system error estimations, and the controller parameters are optimized based on the generalized minimum variance method, to achieve asymptotic tracking of a given speed profile even in the presence of the system errors. Such a control strategy can effectively deal with the uncertainties caused by system errors, improve the control accuracy, and guarantee the safe and reliable operation of high-speed train. To verify the effectiveness of the method proposed in this paper, simulation experiments are conducted by using the CRH380A type high-speed train as the controlled object. Simulation results show that the compensation control method designed in this paper has desired control performance despite the existence of unknown system errors.