Based on the single lane traffic cellular automaton(CA) model introduced by Nagel and Schreckenberg(called NS model), Xue Yu et al proposed an improved single lane traffic CA model by considering the relative motion of vehicles(called i mproved NS model).Several faults in the improved NS model using two examples is pointed out and also another single lane traffic CA model by introducing vehicle _moving_status variable and feedback rule is proposed. These methods help to pre vent vehicle from moving backward and stopping hurry. Numerical simulations are carried out and the results indicate that the deceleration probability and traff ic density have a heavy impact on the evolution process of traffic flow. Under t he condition of high deceleration probability, there may happen local traffic ja ms even with low traffic density. And with a constant deceleration probability, the global free phases and jam phases will appear alternately as the traffic den sity increases to a certain level. The phenomenon is very similar to the propaga tion of wave. The traffic flow is higher in the new model than in the improved N S model. This proves that the stop status of the whole traffic flow has been imp roved.