Considering the condition of having a stationary vehicle ahead, a new one-dimensional cellular automaton model emphasizing high safety is proposed to reduce the probability of rear-end collision in the Nagel-Schreckenberg model. The simulation results reveal the presence of metastable state, nonequilibrium phase transition and hysteresis effects, which have been observed in real traffic. Due to the introduction of the safety probability, traffic flow near the critical density will turn to a synchronized flow at low speed, rather than the jam state. So the probability of rear-end collision will be reduced and the traffic capacity may be increased at high traffic density.