The release of Gaia catalogue is revolutionary to the astronomy of Solar system objects. After some effects such as atmospheric refraction and CCD geometric distortion have been taken into account, the astrometric precision for ground-based telescopes can reach the level of tens of milli-arcseconds (mas). If an object approaches a reference star in a small relative angular distance (less than 100 arcsec), which is called close approach event in this work, the relative positional precision between the object and reference star will be further improved since the systematic effects of atmospheric turbulence and local telescope optics can be reduced. To obtain the precise position of a main-belt asteroid in an close approach event, a second-order angular velocity model with time is supposed in the sky plane. By fitting the relationship between the relative angular distance and observed time, we can derive the time of maximum approximation and calculate the corresponding position of the asteroid. In practice, five nights' CCD observations including 15 close approach events of main-belt asteroid (702) Alauda are taken for testing by the 1 m telescope at Yunnan Observatory, China. Compared with conventional solutions, our results show that the positional precision significantly improves, which reaches better than 4 mas, and 1 mas in the best case when referenced for the Jet Propulsion Laboratory (JPL) ephemeris in both right ascension and declination.