Under the constant temperature and pressure boundary conditions, a mathematical model of fuel washing was established based on the numerical integration method. Firstly, the validity of the model was verified by comparing the calculated results obtained from the model of Boeing 747 with the experimental data published in foreign literatures, showing good agreement of the results. Secondly, the model of Boeing 737 central wing fuel tank was chosen as a research objective, the inerting gas was distributed by uniform and non-uniform ways; when the flow of inerting gas was distributed by volume and quantity ways, the changes of oxygen concentration with time and volumetric tank exchange (VTE) were calculated. The results shows that, when inerting is completed, uniform inlet with nitrogen-rich air distributed by volume costs the shortest inerting time, and uniform inlet with nitrogen-rich air distributed by quantity costs the longest inerting time. The comparison between changes of left side, right side and center in overall average oxygen concentration with VTE shows that non-uniform inlet is better than uniform inlet.