Nowadays there are many methods to solve fractional order differential equation, including finite difference method, finite element method, meshless method etc. In many methods of solution to ordinary differential equations, the most important one is predictor corrector. Based on the atmospheric diffusion theory, considering various influence factors of nuclear radiation substance diffusion which includes wind speed, wind direction, rainfall and other factors, this paper establishes a predictor corrector model, the result of which is solved by using MATLAB. Then the paper obtains favorable result which is in compliance with actual monitoring data. Finally, based on the model, the paper analyzes the diffusion from a global perspective and reaches the conclusions that nuclear dispersal has little effect on the southeast coast of China and the west coast of the United States.