  We investigate the possibility of observing the direct CP violation in the
decay modes $B^- \to D^0 D_s^-$ and $D^0 D^-$ within the Standard Model.
Including the contributions arising from the tree, annihilation, QCD as well as
electroweak penguins with both time- and space-like components, we find that
the direct CP asymmetry in $B^- \to D^0 D_s^-$ is very small $\sim 0.2$ % but
in $B^- \to D^0 D^- $ decay it can be as large as 4%. Approximately $10^7$
charged $B$ mesons are required to experimentally observe the CP asymmetry
parameter for the later case. Since this is easily accessible with the
currently running B factories, the decay mode $B^- \to D^0 D^-$ may be pursued
to look for CP violation.
