  We investigate the strong coupling constants of $D D A$, $D^{*}D^{*}A$ and
$D^{*} D A$ vertices in the framework of the light-cone QCD sum rules, where
$A$ is an axial vector meson such as $a_1, b_1, K_{1A}, K_{1B}, K_1(1270)$ and
$K_1(1400)$. Using the strong coupling constants of $D_s D K_1$, $D_s^* D K_1$
and $D_s^* D^* K_1$ vertices for $K_1(1270)$ and $K_1(1400)$ mesons, we
evaluated the branching ratios of the non-leptonic decays $B^0\to
{K}_{1}^{+}(1270,1400) \pi^-$. Our results for the branching ratios of these
decays are a good agreement with the experimental values.
