In this work, we present the lattice QCD calculation of the distribution amplitudes of longitudinally and transversely polarized vector mesons $K^*$ and $\phi$ using large momentum effective theory. This investigation was carried out on three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ) action, at physical pion mass and $a \approx \{0.06, 0.09, 0.12\}$ fm lattice spacings, choosing three different hadron momenta $\{1.29, 1.72, 2.15\}$ GeV. The bare correlations are renormalized by a hybrid scheme proposed recently. The finial results are derived after the extrapolation to the continuum and infinite momentum limit. The finial results will provide crucial $ab$ $initio$ theory inputs for analyzing pertinent exclusive processes.