This article deals with the characteristic of the multiple velocity difference car-following model. We obtain the stability conditions of the model by using the linear stability analysis, and find that the stable region is apparently enlarged by adjusting the information about the multi-velocity difference. We study the nonlinear characteristics of the model by applying the reductive perturbation method. We obtain the Burgers equation and the modified Korteweg-de-Vries (mKdV) equation around the critical point and the Korteweg-de-Vries (KdV) equation near the neutral stability line in the stable region and the unstable region and the metastable region. The soliton solution of Burgers equation, the kink-antikink solution of mKdV equation, and the solition solution of KdV equation describe the traffic jams.