  In this paper, we study the OZI-allowed two-body strong decays of $3^-$
heavy-light mesons. Experimentally the charmed $D_{3}^{\ast}(2760)$ and the
charm-strange $D_{s3}^{\ast}(2860)$ states with these quantum numbers have been
discovered. For the bottomed $B(5970)$ state, which was found by the CDF
Collaboration recently, its quantum number has not been decided yet and we
assume its a $3^-$ meson in this paper. The theoretical prediction for the
strong decays of bottom-strange state $B_{s3}^\ast$ is also given. The
relativistic wave functions of $3^-$ heavy mesons are constructed and their
numerical values are obtained by solving the corresponding Bethe-Salpeter
equation with instantaneous approximation. The transition matrix is calculated
by using the PCAC and low energy theorem, following which, the decay widths are
obtained. For $D_{3}^\ast(2760)$ and $D_{s3}^\ast(2860)$, the total strong
decay widths are 72.6 MeV and 47.6 MeV, respectively. For $B_3^\ast$ with
$M=5978$ MeV and $B_{s3}^\ast$ with $M=6178$ MeV, their strong decay widths are
22.9 MeV and 40.8 MeV, respectively.
