  We systematically study the semileptonic decays of ${\bf B_c} \to {\bf
B_n}\ell^+ \nu_{\ell}$ in the light-front constituent quark model, where ${\bf
B_c}$ represent the anti-triplet charmed baryons of
$(\Xi_c^0,\Xi_c^+,\Lambda_c^+)$ and ${\bf B_n}$ correspond to the octet ones.
We determine the spin-flavor structures of the constituents in the baryons with
the Fermi statistics and calculate the decay branching ratios (${\cal B}$s) and
averaged asymmetry parameters ($\alpha$s) with the helicity formalism. In
particular, we find that
  ${\cal B}( \Lambda_c^+ \to \Lambda e^+ \nu_{e}, ne^+ \nu_{e})=(3.55\pm1.04,
0.36\pm0.15)\%$,
  ${\cal B}( \Xi_c^+ \to \Xi^0 e^+ \nu_{e},\Sigma^0 e^+ \nu_{e},\Lambda e^+
\nu_{e})=(11.3\pm3.35), 0.33\pm0.09,0.12\pm0.04\%$
  and ${\cal B}( \Xi_c^0 \to \Xi^- e^+ \nu_{e},\Sigma^- e^+
\nu_{e})=(3.49\pm0.95,0.22\pm0.06)\%$.
  Our results agree with the current experimental data. Our prediction for
${\cal B}( \Lambda_c^+ \to n e^+ \nu_{e})$ is consistent with those in the
literature, which can be measured by the charm-facilities, such as BESIII and
BELLE. Some of our results for the $\Xi_c^{+(0)}$ semileptonic channels can be
tested by the experiments at BELLE as well as the ongoing ones at LHCb and
BELLEII.
