Rainfall decreases road adhesion coefficient and sight distance of drivers, these can easily lead to traffic accidents which affect the road traffic efficiency. To study the vehicle lane-changing behavior under rainfall conditions, the adhesion coefficient parameter and drivers' reaction delay time parameter are introduced into the safety distance model. Based on the relationship between rainfall intensity and the water film thickness as well as the relationship among the road adhesion coefficient, water film thickness, and vehicle speed, the influence of rainfall on the road adhesion coefficient is quantified. And based on the relationship between visibility distance under rainfall condition and safe distance upon stopping sight distance, the influence of rainfall on drivers' reaction delay time is quantified. Therefore, the safety distance is different under different rainfall conditions and vehicle speed, it no longer is a fixed value like in other lane-changing models by quantifying the two parameters. The improved lane-changing model is established by considering the influence of the speed difference on vehicle lane-changing behavior; the speed difference is not only existing between the research vehicle and the adjacent lane vehicle ahead, but also between the research vehicle and the adjacent lane after the car. And the safety distance model including the two parameters is embedded in the improved lane-changing model by the lane-changing rules. For the three-lane traffic, the lane-changing rules which take into consideration the safety distance and the speed difference are established respectively for each lane, and the simulation analysis is conducted using cellular automata based on the above mentioned rules. Simulation results show that in the medium density the lane-changing rates in the rain condition are significantly lower compared with sunny days, the biggest drop is about 25%. Through comparison and analysis of the space-time diagrams and the speed-time curve of one vehicle at different traffic density on rain days and sunny days, the improved model redisplays the phenomenon of free flow, free flow into dynamic blocking flow in the absence of external cause, and the phenomenon of vehicles stopping and going under blocking flow. In the medium and high densities, the rain causes more traffic congestion, and the frequency and duration of traffic congestion in space-time diagram increase accordingly; the low speed and the speed of zero state increase gradually in the speed-time curve.