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In this paper, a new car-following model is proposed with the consideration of the incorporating timid and aggressive behaviors on single lane. The linear stability condition with the incorporating timid and aggressive behaviors term is obtained. Numerical simulation indicates that the new car-following model can estimate proper delay time of car motion and kinematic wave speed at jam density by considering the incorporating the timid and aggressive behaviors. The results also show that the aggressive behavior can improve traffic flow while the timid behavior deteriorates traffic stability, which means that the aggressive behavior is better than timid behavior since the aggressive driver makes rapid response to the variation of the velocity of the leading car. Snapshot of the velocities also shows that the new model can approach approximation to a wide moving jam.