The velocity differences between the galaxies and the underlying dark matter have been suggested by recent theoretical halo modeling and results in the N-body simulations. However, the origin of such velocity differences are not well understood in literature, especially for the case between the central galaxies and the host dark matter halos, which means that the central galaxies have not settled down in the halo centers even for the local universe. In this talk, I will present our recent results of understanding the galaxy-halo connection from the velocity field using the high-resolution Illustris hydrodynamic simulations. I'll also talk about the implication of this work to the constraints of cosmology and the galaxy formation and evolution models.