In this paper, an adaptive iterative learning control (AILC) strategy for high-speed trains with unknown speed delays and control input saturations is designed to address speed trajectory tracking problem. The train motion dynamics containing nonlinearities and parametric uncertainties are formulated as a nonlinearly parameterized system. Instead of estimation or modeling of train delays, an unknown time-varying delay term is integrated into the speed on delay analysis by means of Lyapunov-Krasovskii function. Through rigorous analysis, it is confirmed that the proposed AILC mechanism can guarantee convergence of train speed to the desired profile during operations repeatedly. Case studies with numerical simulations further verify the effectiveness of the proposed approach.Note to Practitioners-High-speed railway system (HRS), as a practical engineering system, is inevitably nonlinear subject to the aerodynamic problems, the limitation of actuators and the timedelay occurrence. However, there is little work done to consider those factors simultaneously. This motivates the work of this note. Based on the outstanding repetitive operation pattern of a train, the control strategies of speed trajectory tracking are addressed in the framework of ILC, which is primarily a data driven modelfree control method. To avoid the passenger's discomfort with the speedup of trains, the adaptive control is employed in the iteration domain to solve the nonlinearities and parametric uncertainties in train motion dynamics. By constructing a robust term in the controller, the time-varying speed delays, which may occur frequently during operation process arising from weather conditions, construction works, human factors and regulation managements, etc., are compensated. To further enhance the applicability, the corresponding control scheme under traction/braking force constraint is also considered. Although the effectiveness of the novel AILC-based train control method has been proved through the rigorous theoretical analyses, the field experiments have not been carried out yet. Some other practical concerns, such as operationdepended disturbances and actuator failures in train operations, should be further studied.Index Terms-Adaptive iterative learning control, composite energy function, input saturations, time-varying speed delays, highspeed train, train control.