Abstract This paper describes some basic results obtained in our research on the orbital evolutioin of near Earth asteroids (NEAs) over the past several years. We emphasize the use of the reasonable dynamical model and an effective algorithm in the numerical work. The model includes all possible factors that affect the motion of NEAs, including the gravitation of all the larger bodies and the four larger main-belt asteroids, the effect of oblateness of the bodies and the post-Newtonian effect of the solar gravitation. By using the orbital elements of the Moon as the variables in the integration a single step size can be used. The times and distances of closest approach for NEAs that approach the Earth during the 21st century are calculated and are found to agree closely with the results published by the MPC.