We present the first determination of the pairwise velocity dispersion of galaxies at different luminosity with the final release of the Two-Degree Field Galaxy Redshift Survey (2dFGRS). Our result surprisingly shows that the random velocities of the faint galaxies are very high, around $700 {\rm km\,s}^{-1}$, reaching similar values as the brightest galaxies. At intermediate luminosities slightly brighter than the characteristic luminosity $M_*$, the velocities exhibit a well defined steep minimum near $400 {\rm km\,s}^{-1}$. The result challenges the current halo model of galaxies of Yang et al. that was obtained by matching the clustering and luminosity function of 2dFGRS, and can be an important constraint in general on theories of galaxy formation, e.g., the semi-analytical model. Combining the observed luminosity dependence of clustering, our result implies that quite a fraction of faint galaxies are in massive halos of galaxy clusters as the brightest ones, but most of the $M_*$ galaxies are in galactic halos.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html