In recent years, the experimental results about the ratio of the branching ratios $$R_{D^{(*)}}$$ $R_{D^{(\ast )}}$ and $$R_{K^{(*)}}$$ $R_{K^{(\ast )}}$ , which are in the semileptonic $$b\rightarrow c l \bar{\nu }_{l}$$ $b\to cl{\overline{\nu }}_l$ and $$b\rightarrow s l^+l^-$$ $b\to s{l}^{+}{l}^{-}$ decays, have been observed to deviate from the Standard Model prediction by $$1.4\sigma $$ $1.4\sigma$ , $$2.5\sigma $$ $2.5\sigma$ , $$2.4\sigma $$ $2.4\sigma$ and $$2.2\sigma $$ $2.2\sigma$ respectively. Motivated by these anomalies and by the abundant $$B^*$$ $B^{\ast }$ data samples, we investigate possible New Physics effects of the vector leptoquark in the semileptonic decay $$\bar{B}^*_{u,d,s,c} \rightarrow V \tau ^-\bar{\nu }_{\tau }$$ ${\overline{B}}_{u,d,s,c}^{\ast }\to V{\tau }^{-}{\overline{\nu }}_{\tau }$ ( $$V=D^*_{u,d,s},J/\psi $$ $V=D_{u,d,s}^{\ast },J/\psi$ ). which is induced by $$b\rightarrow c \tau ^-\bar{\nu }_{\tau }$$ $b\to c{\tau }^{-}{\overline{\nu }}_{\tau }$ at the quark level. Using the best fit solutions for the new operator Wilson coefficients and the relevant form factors which are obtained in the light-front quark model, we find that (i) the contributions of the vector leptoquark to $$d{\varGamma }^{(L)}/dq^2(\bar{B}^*_{u,d,s,c} \rightarrow V \tau ^-\bar{\nu }_{\tau })$$ $d{\Gamma }^{\left(L\right)}/d{q}^2({\overline{B}}_{u,d,s,c}^{\ast }\to V{\tau }^{-}{\overline{\nu }}_{\tau })$ and $$R^{*(L)}_{V}(q^2)$$ $R_V^{\ast \left(L\right)}\left(q^2\right)$ to be significant; (ii) the two best fit solutions in the vector leptoquark are indistinguishable from each other and give similar amounts of enhancements to these two observables; (iii) both two cases of the vector leptoquark give nearly same results as those of the Standard Model for $$A_{FB}^{\tau }(q^2)$$ $A_{\mathrm{FB}}^{\tau }\left(q^2\right)$ , $$P_{\tau }(q^2)$$ $P_{\tau }\left(q^2\right)$ and $$F_{L}^{*V}(q^2)$$ $F_L^{\ast V}\left(q^2\right)$ . We hope that the numerical results in this work will be tested in the future high energy experiments.