In this work, we focus on the light vector meson leading-twist longitudinal distribution amplitudes (DAs) ${\varphi }_{2;V}^{\parallel }(x,\mu )$ with $V=\rho ,K^{*},\varphi$. A new scheme of QCD sum rule research with respect to DA suggested in 2021 by us is adopted. With an improved sum rule formula, the $\xi$-moments $⟨{\xi }^n{⟩}_{2;V}^{\parallel }$ up to tenth order are calculated. In which, $⟨{\xi }^2{⟩}_{2;\rho }^{\parallel }={0.225}_{-0.012}^{+0.013}$, $⟨{\xi }^1{⟩}_{2;K^{*}}^{\parallel }=-{0.0228}_{-0.0040}^{+0.0042}$, $⟨{\xi }^2{⟩}_{2;K^{*}}^{\parallel }={0.217}_{-0.007}^{+0.007}$, $⟨{\xi }^2{⟩}_{2;\varphi }^{\parallel }={0.209}_{-0.020}^{+0.020}$, and the corresponding Gegenbauer moments $a_{2;\rho }^{2;\parallel }={0.074}_{-0.036}^{+0.039}$, $a_{2;K^{*}}^{1;\parallel }=-{0.038}_{-0.007}^{+0.007}$, $a_{2;K^{*}}^{2;\parallel }={0.050}_{-0.019}^{+0.020}$, $a_{2;\varphi }^{2;\parallel }={0.027}_{-0.058}^{+0.058}$ at the scale $\mu = 1~{\rm GeV}$, respectively. By fitting those $⟨{\xi }^n{⟩}_{2;V}^{\parallel }(n=1,2,\cdots ,10)$ with the least squares method, the behaviors of leading-twist longitudinal DAs for $\rho ,K^{*},\varphi$ are determined. In addition, we also analyze the impact of incorporating different numbers of $\xi$-moments into the fitting on the stability and reliability of the obtained DAs. Be different from the pion leading-twist DA, we find that the higher-order moments do not significantly change the reconstructed shapes of ${\varphi }_{2;V}^{\parallel }(x,\mu )$. Further, we recalculate the transition form factors and branching ratios of the $D\to (\rho ,K^{*})$, $D_s\to \varphi$ semi-leptonic decay processes.