With the consideration of the effect of driver anticipation behavior on traffic flow, a new one-dimensional lattice model is proposed. The linear stability condition of the presented model is obtained by employing the linear stability theory. The density wave near the critical stable point is investigated analytically with the nonlinear analysis method. The results show that the occurrence of traffic jamming transitions can be described by the kink-antikink solution of the modified Korteweg-de Vries (mKdV) equation. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the effect of driver anticipation behavior is considered.