In response to the problem that ground-based optical monitoring systems cannot monitor near-Earth asteroids which are too close to the Sun on the celestial sphere, we raise a method that tracks and determines the orbit of asteroids by Distant Retrograde Orbit (DRO) platforms with optical monitoring. Through data filtering by visibility analysis and the initial orbit information of the asteroids provided by Jet Propulsion Laboratory (JPL), the asteroids' orbits are determined and compared with the reference orbit. Simulation results show that with a measurement accuracy of two arcseconds and an arc length of three years, the orbit determination accuracy of the DRO platform for near-Earth asteroids selected in the simulation example can reach tens of kilometers, especially the asteroids with Atira orbits to an accuracy of fewer than ten kilometers. In conclusion, the near-Earth asteroids monitoring systems based on DRO platforms are capable to provide sufficient monitoring effectiveness which enables precise tracking of the target asteroids and forecast of their positions.