We study the impact of vector leptoquarks on the recent anomalies in semileptonic $B$ meson decays such as $R_K$ and $R_{D^{(*)}}$ etc. We constrain the leptoquark couplings by using the existing data on the branching ratios of $B_s \to l^+ l^-$ and $\bar{B} \to X_s l^+ l^-$ processes, where $l=e,\mu,\tau$. We estimate the branching ratios of $\bar B \to D^{(*)} l \bar \nu_l$ processes using the constrained leptoquark parameter space. We also investigate the possibility of simultaneous explanation of $R_{D^{(*)}}$, $R_K$ anomalies in this model.