  Using a combination of N-body simulations with different resolutions, we
study in detail how the concentrations of cold dark matter (CDM) halos depend
on halo mass at different redshifts. We confirm that halo concentrations at the
present time depend strongly on halo mass, but our results also show marked
differences from the predictions of some early empirical models. Our main
result is that the mass dependence of the concentrations becomes weaker at
higher redshifts, and at z >~ 3 halos of mass greater than 10^{11} Msun/h all
have a similar median concentration, c ~ 3.5. While the median concentrations
of low-mass halos grow significantly with time, those of massive halos change
only little with redshifts. These results are quantitatively in good agreement
with the empirical model proposed by Zhao et al. which shows that halos in the
early fast accretion phase all have similar concentrations.
