Based on the NaSch cellular automaton traffic model, a new one_dimensional cellular automaton model (called SDNaSch model, for short) is proposed through prefer entially considering the sensitive behaviour of drivers, in which the randomizat ion brake is arranged before the deterministic deceleration. According to the ne w update rules of the evolution of vehicles, numerical simulation is conducted a nd leads to some new results. The fundamental diagram obtained by the simulation shows that the traffic capacity of a road is enhanced and closer to the observe d data compared with that of the NaSch model. It is found from the fundamental d iagram that there exist two branches in some density regions, which illustrates the existence of the metastable state near the critical point and the phase sepa ration. According to the evolution pattern of the vehicle speed in space and tim e, the wide moving jams is reproduced with the phase transitions between free fl ow and wide moving jams. With the consideration of the actual traffic situation, i.e., some drivers being sensitive and following the new rules, while others be ing not and following the original NaSch rules, the corresponding simulation ver ifies the remarkable effect of the sensitive driving factor on the characteristi cs of traffic flows. The traffic capacity rises along with the increase in the f raction of sensitive drivers.