A quasiclassical trajectory study with the sixth-order explicit symplectic algorithm for the N(4S)+O2 (X3∑-g ) →NO (X2Ⅱ)+O(3P) reaction has been reported by employing a new ground potential energy surface. We have discussed the influence of the relative translational energy, the vibrational and rotational levels of O2 molecules on the total reaction cross section. Thermal rate constants at temperatures 300, 600, and 1000 K determined in this work for the reaction are 4.4 × 107, 1.8 × 1010, and 3.1 × 1011 cm3mol-1s-1, respectively. It is found that they are in better agreement with the experimental data than previous theoretical values.