  Using the next-to-leading order low energy effective Hamiltonian, the CP
asymmetries for the $B_{c}$ meson decays into meson pair are calculated in the
spectator approximation. We do not compute the hadronic matrix elements
directly, instead, we use the amplitude ratios to estimate the CP asymmetries.
This is quite,different from the previous works in the literature. The values
of the momentum squared carried by the virtual particles in timelike penguin
dirgrams are also carefully discussed. From our calculated results, the best
decay modes to observe CP violation in $B_{c}$ decays would be $B_{c}^-\to{\bar
D}^{*0}K^{*-}$, ${\bar D}^{0}K^{*-}$, ${\bar D}^{*0} K^{-}$, ${\bar
D}^{0}K^{-}$ and $B_{c}^-\to{\eta}_{c}D^{-}$, which need about $10^8$ of
$B_{c}^{\pm}$ events in experiment.
