  Many $P-$wave mixing heavy-light $1^+$ states have not been discovered by
experiment, some of them have been discovered but without the information of
width, or with large uncertainty widths. In this paper, we study the strong
decays of $P-$wave mixing heavy-light $1^+$ states $D^0$, $D^\pm$, $D_s^\pm$,
$B^0$, $B^\pm$ and $B_s$ by the improved Bethe-Salpeter(B-S) method in two
conditions of mixing angle $\theta$: one is $\theta=35.3^\circ$; another is
considering the correction to mixing angle $\theta=35.3^\circ+\theta_1$. And we
get some valuable predictions of the strong decay widths:
$\Gamma(D_1^{\prime0})=232$ MeV, $\Gamma(D_1^0)=21.5$ MeV,
  $\Gamma(D_1^{\prime\pm})=232$ MeV, $\Gamma(D_1^\pm)=21.5$ MeV,
$\Gamma(D_{s1}^{\prime\pm})=0.0101$ MeV, $\Gamma(D_{s1}^{\pm})=0.950$ MeV,
$\Gamma(B_1^{\prime\pm})=263$ MeV, $\Gamma(B_1^{\pm})=16.8$ MeV,
$\Gamma(B_{s1}^{\prime})=0.01987$ MeV and $\Gamma(B_{s1})=0.412$ MeV. We find
that the decay widths of $D_{s1}^{\pm}$ and $B_{s1}$ are very sensitive to the
mixing angle. And our results will provide the theoretical assistance by the
future experiments.
