To reasonably simulate the stochastic traffic load on bridge site, a new cellular automata based on car following theory is proposed. Firstly, a new transformable cell which considers the vehicle as the core is proposed. The precise axle gap and axle weight are incorporated into the cell to fulfill the goal of precise vehicle load simulation. Then, the car following theory is introduced to propose the new transition rules, and the acceleration of each vehicle can be calculated based on the proposed transition rules. Finally, new boundary rules based on Weigh in Motion (WIM) is proposed. The vehicle sequence of any time period which matches the real one can be generated based on the WIM data, based on which the initial states of the vehicles to enter the road can be determined. Based on the proposed transition rules and the boundary rules, the spatiotemporal position of vehicles can be simulated, and the stochastic traffic load can be simulated with consideration of the new cell. The proposed model is validated using real WIM data, and the results indicate that the proposed new cell can precisely simulate the vehicle load. The proposed transition rules can compute the specific acceleration for each vehicle, and free driving and car following can be simulated. With simultaneously using the vehicle sequence generation method and the transition rules, the real traffic load of any time period can be reconstructed. The proposed CA model can be applied to simulate the stochastic traffic load of any time period on bridge site. With considering the precise axle load and reasonable traffic flow, the stochastic traffic load on bridge site can be successfully simulated.