  We study the CP violation in two-body nonleptonic decays of $B_c$ meson. We
concentrate on the decay channels which contain at least one excited heavy
meson in the final states. Specifically, the following channels are considered:
$B_c\to c\bar c(2S, 2P)+\bar cq(1S, 1P)$, $B_c\to c\bar c(1S)+\bar cq(2S, 2P)$,
$B_c\to c\bar c(1P)+\bar cq(2S)$, $B_c\to c\bar c(1D)+\bar cq(1S, 1P)$, and
$B_c\to c\bar c(3S)+\bar cq(1S)$. The improved Bethe-Salpeter method is applied
to calculate the hadronic transition matrix element. Our results show that some
decay modes have large branching ratios, which is of the order of $10^{-3}$.
The CP violation effect in $B_c \rightarrow \eta_c(1S)+D(2S)$, $B_c \rightarrow
\eta_c(1S)+D_0^{*}(2P)$, and $B_c \rightarrow J/\psi+D^{*}(2S)$ are most likely
to be found. If the detection precision of the CP asymmetry in such channels
can reach the $3\sigma$ level, at least $10^7$ $B_c$ events are needed.
