  We take into account the $1/m_Q$ corrections upto $1/N_c$ order in the
heavy-meson-soliton bound state approach for heavy baryons. With these
corrections, the mass spectra of baryons with $c$-quark as well as of those
with $b$-quark are well reproduced. For charmed baryons, however, the
correction to the mass spectra amounts to about 300 MeV, which is not small
compared to the leading order binding energy, $\sim 800$ MeV.
