  We investigate the charm hadron production in relativistic heavy-ion
collisions with the quark combination model. The $p_{T}$ dependencies of the
charm baryon to meson ratios such as
$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{0}+\bar{D}^{0}}$,
$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D^{+}+D^{-}}$ and
$\frac{\Lambda_{c}+\bar{\Lambda}_{c}}{D_{s}^{+}+D_{s}^{-}}$ in Au+Au collisions
at 200 GeV are obtained. The charm baryon enhancement in the intermediate
$p_{T}$ range is very prominent, which further, together with the strangeness
enhancement, affect the charm hadron ratios and lead to a $\sim17%$ larger
charm cross-section given by PHENIX. The dependencies of the charm hadron
ratios on energy, centrality, and other parameters are also investigated.
Predictions of the charm hadron ratios for the upgrade of RHIC and for LHC are
presented.
