The human drivers in a real world decide and act according to their experience, logic, and judgments. In contrast, mathematical models act according to mathematical equations that ensure the precision of decision to take. However, these models do not provide a promising simulation and they do not reflect the human behaviors. In this context, we present in this paper a completely artificial intelligence anticipation model of car-following problem based on fuzzy logic theory, in order to estimate the velocity of the leader vehicle in near future. The results of experiments, which were conducted by using Next Generation Simulation (NGSIM) dataset to validate the proposed model, indicate that the vehicle trajectories simulated based on the new model are in compliance with the actual vehicle trajectories in terms of deviation and gap distance. In addition, the road security is assured in terms of harmonization between gap distance and security distance.