We studied a next neighbor lattice model by considering the delay of driver′s response to the traffic flow. The stability criterion was derived by the linear stability analysis. The evolution of density wave has been analyzed by using the perturbation method. The results show that the occurrence of traffic jamming transitions is described by the kink and anti kink solutions of the mKdV equation. Moreover, we studied the influence of the delay of driver′s response and the flux difference on the model stability.