In this paper, we propose a new cellular automaton (CA) model for train movement simulations under mixed traffic conditions. A kind of control strategy is employed for trains to reduce energy consumption. In the proposed CA model, the driver controls the train movements by using some updated rules. In order to obtain a good insight into the evolution behaviours of the rail traffic flow, we investigate the space-time diagram of the rail traffic flow and the trajectories of the train movements. The numerical simulation results demonstrate that the proposed CA model can well describe the dynamic behaviours of the train movements. Some complex phenomena of train movements can be reproduced, such as the train delay propagations, etc.