When a driver is sensing headway,there exists a time-varying delay,and the sensitivity of the driver changes with the speed and the headway within a certain range.In order to accurately describe the running state of vehicles,on the basis of coupled-map car-following model,a new coupled-map fuzzy car-following model with timedelays is proposed,and the stability of the new car-following model is investigated.Then,by using Lyapunov function,the sufficient condition of the existence of a fuzzy controller is given.Under this condition,the closed-loop system achieves an asymptotic stability,that is,traffic congestion phenomena can be effectively suppressed.Finally,the fuzzy controller is obtained by solving a linear matrix inequality ( LMI) .Simulation results show that,with the help of the fuzzy controller,the car achieves smaller amplitude of velocity oscillation,faster process of recovering to an equilibrium state,and lower emission of carbon dioxide,which means that this method is effective in suppressing traffic congestion and reducing carbon dioxide emissions.