Abstract: The effects of the nonlinear refraction indexes (n2, n4, n6, n8) on the propagation of the femtosecond high-intensity laser pulse are studied. We consider three models. The first model includes n2, n4, n6, and n8. The second one only includes n2 and n4. The third model includes n2, n4, and n6. Numerical simulations show that the third model cannot properly describe the propagation of the ultra-short high intensity laser pulse, and the index n2 is the most important focusing mechanism at the beginning of the propagation, and n8 and n6 are the most important indexes in the stable propagation stage, and the pulses radius in the first model is almost the same as that in the second model, so does the number of filamentations splitted in the temporal direction. This work is useful in understanding the mechanism of the femtosecond laser pulse propagation in air.