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: $B_cto cbar c(2S, 2P)+bar cq(1S, 1P)$, $B_cto cbar c(1S)+bar cq(2S, 2P)$, $B_cto cbar c(1P)+bar cq(2S)$, $B_cto cbar c(1D)+bar cq(1S, 1P)$, and $B_cto cbar c(3S)+bar cq(1S)$. 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 $3sigma$ level, at least $10^7$ $B_c$ events are needed.
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