The vicinity of traffic signals is one of the most critical areas in road systems. New information technology paradigms like vehicle-to-vehicle and vehicle-to-infrastructure communication are applied to improve traffic operations at intersections; for example, a typical cyber-physical system enables efficient traffic state estimation and traffic modeling. A new model of vehicle cooperative driving under a typical scenario vicinity of traffic signals and Vehicle to X environment was proposed in this paper. Based on the intelligent driver model, the model planned trajectories for vehicles in the vicinity of traffic signals in advance to reduce stopping frequency and travel time and improve the throughput of the road according to traffic conditions, such as signal cycle state, the distance to traffic signals, and the situation regarding adjacent vehicles. In accordance with the relationship between the host vehicle and the surrounding vehicles, the model also planed the cooperative lane changing strategy in this scenario to improve safety and comfort in the process of lane changing. A simulation experiment compared the proposed model with the traditional intelligent driver model, and analyzed its performance in different traffic conditions. The feasibility and superiority of the model were confirmed.