In this paper, we investigate the performance of the well-known optimal velocity car-following model(the OVM) with numerical simulation in describing the acceleration process that is induced by the motion of a ldading car with a pre-specifide speed profile. Results show that this model is to some extent deficient in performing this process. Modification of the OVM to overcome the deficiency is demonstrated. The linear stability for the modified model is analysed. If the linear stability condition can not be satisfied, phase transitions occur on varying the initial homogeneous headway of the traffic flow.