We study the evolution of Lyman Break Galaxies (LBGs) from z=5 to z=0 by tracing the merger trees of galaxies in a large-scale hydrodynamic simulation based on a Lambda cold dark matter model. In particular, we emphasize on the range of properties of the sample selected by the rest-frame V band luminosity, in accordance with recent near-IR observations. The predicted rest-frame V band luminosity function agrees well with the observed one when dust extinction is taken into account. The stellar content and the star formation histories of LBGs are also studied. We find that the LBGs intrinsically brighter than Mv=-21.0 at z=3 have stellar masses of at least 10^9\Msun, with a median of 10^{10}h^{-1}\Msun. The brightest LBGs (Mv

29 pages, including 11 figures, ApJ in press. One reference added