Smog causes low visibility on the road and it can impact the safety of traffic. Modeling traffic in smog will have a significant impact on realistic traffic simulations. Most existing traffic models assume that drivers have optimal vision in the simulations, making these simulations are not suitable for modeling smog weather conditions. In this article, we introduce the Smog Full Velocity Difference Model (SMOG-FVDM) for a realistic simulation of traffic in smog weather conditions. In this model, we present a stadia model for drivers in smog conditions. We introduce it into a car-following traffic model using both psychological force and body force concepts, and then we introduce the SMOG-FVDM. Considering that there are lots of parameters in the SMOG-FVDM, we design a visual verification system based on SMOG-FVDM to arrive at an adequate solution which can show visual simulation results under different road scenarios and different degrees of smog by reconciling the parameters. Experimental results show that our model can give a realistic and efficient traffic simulation of smog weather conditions.