  In this paper, we investigate the tree-dominated $\bar{B}^*_{u,d,s,c} \to V
\ell^- \bar{\nu}_\ell$ ($V=D^*_{u,d}\,,D^*_s\,,J/\psi$ and
$\ell=e\,,\mu\,,\tau$) decays in the Standard Model with the relevant form
factors obtained in the light-front quark model. These decays involve much more
helicity states relative to the corresponding $\bar{B}^* \to P \ell^-
\bar{\nu}_\ell$ and $\bar{B} \to V \ell^- \bar{\nu}_\ell$ decays, and moreover,
the contribution of longitudinal polarization mode ($V$ meson) is relatively
small, $\sim 30\%$, compared with the corresponding $B$ meson decays. We have
also computed the branching fraction, lepton spin asymmetry, forward-backward
asymmetry and ratio $R_V^{\ast(L)}\equiv \frac{\mathcal{B}(\bar{B}^*\to V\tau^-
\bar{\nu}_\tau)}{\mathcal{B}(\bar{B}^*\to V \ell^{\prime-}
\bar{\nu}_{\ell^{\prime}})}$ ($\ell'=e\,,\mu$). Numerically, the branching
fractions of $\bar{B}^* \to V \ell^{\prime-} \bar{\nu}_{\ell^{\prime}}$ decays
are at the level of ${\cal O}(10^{-7})$, and are hopeful to be observed by LHC
and Belle-II experiments. The ratios $R_{D^*\,,D^*_s\,,J/\psi}^{\ast(L)}$ have
relatively small theoretical uncertainties and are close to each other,
$R^{*(L)}_{D^*}\simeq R^{*(L)}_{D^*_s}\simeq R^{*(L)}_{J/\psi} \simeq
[0.26,0.27]~([0.27,0.29])$, which are a bit different from the predictions in
some previous works. The future measurements are expected to make tests on
these predictions.
