We use a 200 $h^{-1}Mpc$ a side N-body simulation to study the mass accretion history (MAH) of dark matter halos to be accreted by larger halos, which we call infall halos. We define a quantity $a_{rm nf}equiv (1+z_{rm f})/(1+z_{rm peak})$ to characterize the MAH of infall halos, where $z_{rm peak}$ and $z_{rm f}$ are the accretion and formation redshifts, respectively. We find that, at given $z_{rm peak}$, their MAH is bimodal. Infall halos are dominated by a young population at high redshift and by an old population at low redshift. For the young population, the $a_{rm nf}$ distribution is narrow and peaks at about $1.2$, independent of $z_{rm peak}$, while for the old population, the peak position and width of the $a_{rm nf}$ distribution both increases with decreasing $z_{rm peak}$ and are both larger than those of the young population. This bimodal distribution is found to be closely connected to the two phases in the MAHs of halos. While members of the young population are still in the fast accretion phase at $z_{rm peak}$, those of the old population have already entered the slow accretion phase at $z_{rm peak}$. This bimodal distribution is not found for the whole halo population, nor is it seen in halo merger trees generated with the extended Press-Schechter formalism. The infall halo population at $z_{rm peak}$ are, on average, younger than the whole halo population of similar masses identified at the same redshift. We discuss the implications of our findings in connection to the bimodal color distribution of observed galaxies and to the link between central and satellite galaxies.
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