Based on the two-lane traffic model proposed by Chowdhury et al., a modified traffic model (R-STCA model, for short) is presented, in which the new symmetric lane changing rules are introduced by considering driving behavioral difference and dynamic headway. After the numerical simulation, a broad scattering of simulated points is exhibited in the moderate density region on the flow-density plane. The synchronized flow phase accompanied with the wide moving jam phase is reproduced. The spatial–temporal profiles indicate that the vehicles move according to the R-STCA model can change lane more easily and more realistically. Then vehicles are convenient to get rid of the slow vehicles that turn into plugs ahead, and hence the capacity increases. Furthermore the phenomenon of the high speed car-following is discovered by using the R-STCA model, which has been already observed in the traffic measured data. All these results indicate that the presented model is reasonable and more realistic.