  It is well known that the final state interaction plays an important role in
the decays of $B$-meson. The contribution of the final state interaction which
is supposed to be long-distance effects, to the concerned processes can
interfere with that of the short-distance effects produced via the tree and/or
loop diagrams at quark-gluon level. The interference may provide a source for
the direct CP violation $\mathcal{A}_{CP}$ in the process $B_{c}^{+}\to
D^{0}\pi^{+}$. We find that a typical value of $\mathcal{A}_{CP}$ when the
final state interaction effect is taken into account can be about -22% which is
different from that without the final state interaction effect. Therefore, when
we extract information on CP violation from the data which will be available at
LHCb and the new experiments in $B$-factories, the contribution from the final
state interaction must be included. This study may be crucial for searching new
physics in the future.
