  In the covariant light-front quark model, we investigate the $B_c\to h_c,
\chi_{c0,1,2}$ form factors. The form factors are evaluated in space-like
kinematic region and are recasted to the physical region by adopting the
exponential parametrization. We also study the semileptonic $B_c$ decays and
find that branching fractions for the $B_c\to (h_c,\chi_{c0,1,2})l\bar\nu
(l=e,\mu)$ decays have the order $10^{-3}$ while branching fractions for
$B_c\to (h_c,\chi_{c0,1,2})\tau\bar\nu_\tau$ are suppressed by one order. These
predictions will be tested at the forthcoming hadron colliders.
