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We investigate the branching ratios and direct CP asymmetries of $B_c^+\toD^0\pi^+$ and $B_c^+\to D^+\pi^0$ decays in the PQCD approach. All the diagramswith emission topology or annihilation topology are calculated strictly. Abranching ratio of $10^{-6}$ and $10^{-7}$ for $B_c^+\to D^0\pi^+$ and$B_c^+\to D^+\pi^0$ decay is predicted, respectively. Because of the differentweak phase and strong phase from penguin operator and two kinds of treeoperator contributions, we predict a possible large direct CP violation:$A^{\rm dir}_{cp} (B_c^\pm \to D^0 \pi^\pm)\approx -50%$ and $A^{\rm dir}_{cp}(B_c^\pm \to D^\pm \pi^0)\approx 25%$ when $\gamma=55^\circ$, which can betested in the coming LHC.Comment: The numerical results have been updated and some errors have been  corrected. (10 pages, 16 figures, revtex4

Study of B c → D π in the perturbative QCD approach