  We make a systematic investigation on the double charm decays of $B_c$ meson,
by employing the perturbative QCD approach based on $k_T$ factorization. It is
found that the non-factorizable emission diagrams are not negligible in these
channels. We predict the branching ratios of these $B_c$ decays and also the
transverse polarization fractions of $B_c\rightarrow D_{(s)}^{*+}\bar D^{*0},
D_{(s)}^{*+}D^{*0}$ decays, % where V denote the vector $D^*_{(s)}$ meson.
  We find that the magnitudes of the branching ratios of the decays
$B_c\rightarrow D_s\bar{D}^0$ and $B_c\rightarrow D_sD^0$ are very close to
each other, which are well suited to extract the Cabibbo-Kobayashi-Maskawa
angle $\gamma$ through the amplitude relations. In addition, a large transverse
polarization contribution that can reach $50%\sim 60%$ is predicted in some of
the $B_c$ meson decay to two vector charmed mesons.
