In recent years, the experimental results about the ratio of the branching ratios $$R_{D^{(*)}}$$
R
D
(
∗
)
and $$R_{K^{(*)}}$$
R
K
(
∗
)
, which are in the semileptonic $$b\rightarrow c l \bar{\nu }_{l}$$
b
→
c
l
ν
¯
l
and $$b\rightarrow s l^+l^-$$
b
→
s
l
+
l
-
decays, have been observed to deviate from the Standard Model prediction by $$1.4\sigma $$
1.4
σ
, $$2.5\sigma $$
2.5
σ
, $$2.4\sigma $$
2.4
σ
and $$2.2\sigma $$
2.2
σ
respectively. Motivated by these anomalies and by the abundant $$B^*$$
B
∗
data samples, we investigate possible New Physics effects of the vector leptoquark in the semileptonic decay $$\bar{B}^*_{u,d,s,c} \rightarrow V \tau ^-\bar{\nu }_{\tau }$$
B
¯
u
,
d
,
s
,
c
∗
→
V
τ
-
ν
¯
τ
($$V=D^*_{u,d,s},J/\psi $$
V
=
D
u
,
d
,
s
∗
,
J
/
ψ
). which is induced by $$b\rightarrow c \tau ^-\bar{\nu }_{\tau }$$
b
→
c
τ
-
ν
¯
τ
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
Γ
(
L
)
/
d
q
2
(
B
¯
u
,
d
,
s
,
c
∗
→
V
τ
-
ν
¯
τ
)
and $$R^{*(L)}_{V}(q^2)$$
R
V
∗
(
L
)
(
q
2
)
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
FB
τ
(
q
2
)
, $$P_{\tau }(q^2)$$
P
τ
(
q
2
)
and $$F_{L}^{*V}(q^2)$$
F
L
∗
V
(
q
2
)
. We hope that the numerical results in this work will be tested in the future high energy experiments.