The main-belt asteroids are generally considered as the principal source for the near-Earth asteroids (NEAs). The ESA astrometric mission Gaia, due for launch in late 2011, will observe a very large number of asteroids (∼300,000 brighter than V = 20), the majority lying in the main-belt and with an unprecedented positional precision (at the sub-milliarcsecond level). Such high precision astrometry will enable to derive direct measures of the masses of the largest asteroids of which their precise determination will be of utmost significance for the knowledge of physical properties of asteroids. The method for computing the masses is based on the analysis of orbital perturbations during close encounters between massive asteroids (perturbers) and several smaller minor planets (targets). From given criteria of close approaches selection, we give the list of asteroids for which the mass can be determined, and the expected precision of these masses at mission completion.