As the rapid development of smart cities, autonomous vehicles are considered to be the future ground transportation measure which provides many benefits over traditional human-driving vehicles. However, there will be decades before the autonomous vehicles fully penetrate, during when human-drivers will share the same road systems with the autonomous vehicles, where the majority of accidents associated with autonomous vehicles are induced by the operation inconsistency of human drivers, which can be avoided if there is communication between the autonomous vehicles and the infrastructure (V2I). This study develops cumulative-anticipative car-following (CACF) model for autonomous vehicles based on the Cooperate Adaptive Cruise Control/ Adaptive Cruise Control (CACC/ACC) model by considering cumulative influences from multiple preceding vehicles. The simulation results from 128 simulation runs using the micro-simulator VISSIM showed that the CACF model can improve the safety and traffic congestions compared to the Wiedemann 99, the ACC, and the CACC models.