Car-following behaviour is an important problem in terms of road safety, since it represents, alone, almost 70% of road accidents caused by not maintaining a safe braking distance between the moving cars. The inappropriate anticipation of drivers to keep safety distance is the main reason for accidents. In this study, the authors present an artificial intelligence anticipation model for car-following problem based on a fuzzy logic approach. This system will estimate the velocity of the leading vehicle in the near future. Moreover, they have replaced the old methods used in the third step of fuzzy logical approach, the defuzzification, by a novel method based on a metaheuristic algorithm, i.e. Tabu search, in order to adapt effectively to the environment's instability. The results of experiments, conducted using the next generation simulation 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 estimated velocities. Moreover, they show that the proposed model guarantees road safety in terms of harmonisation between the gap distance and the calculated safety distance.