gauge configurations produced for light-hadron spectrum [7]. Furthermore, unlike other methods previously applied, there is no need of multi-loop perturbative calculation on the lattice, which is so complicated that one typically has to develop automated tool dedicated for a given lattice action. Finite volume effect is negligible for VPF at relatively large Q $^{2}$, and discretization effect is carefully studied and is shown to be under control. The method therefore provides a reliable and economical way to extract the most important parameter of QCD, i.e. α$_{s}$ . A similar idea has also been applied for the charmonium two-point function to determine α$_{s}$ as well as charm quark mass [9]. In this work, we extend our previous study to the case of realistic three-flavor QCD with dynamical light and strange quarks. We also improve the calculation by employing the conserved current for the overlap fermion [10], which simplifies the possible form of the two-point function as it satisfies the Ward-Takahashi (WT) identity on the lattice. The extraction of VPF is thus made more straightforward. The determination of the strong coupling constant uses the continuum perturbative QCD formula up to four loops and OPE up to 1 /Q 4 terms. The value of the quark condensate is calculated independently and used as an input in this work. The result is translated to the common definition, i.e. α (5) s ( M$_{Z}$ ), the strong coupling constant of five-flavor QCD in the MS scheme at the Z boson mass scale. Numerical simulations of lattice QCD are carried out with 2+1-flavors of dynamical fermions described by the overlap fermion formulation [11, 12]. We have data at a single lattice spacing with the inverse lattice spacing a − 1 = 1.83(1) GeV estimated using the static quark potential with an input for the Sommer scale r$_{0}$ = 0.49 fm (the associated error for this is discussed later). The lattice volume is 16 $^{3}$× 48, which leads to the physical volume about (1.8 fm) $^{3}$× (5.4 fm). The gauge configurations are generated in the course of the dynamical overlap fermion simulations by the JLQCD and TWQCD collaborations [13]. The set of up and down quark masses m$_{ud}$ covers the range of (0.2–0.8) m phys s and the set of the strange quark mass m$_{s}$ covers the range of (1.0–1.3) m phys s with m phys s the physical strange quark mass. The valence quark mass in the calculation of VPF is set equal to the up and down sea quark mass. For each combination of m$_{ud}$ and m$_{s}$ , we use 260 configurations, each of which is separated by 100 HMC trajectories. Global topological charge of the gauge configurations is fixed to zero, which may induce small finite size effect for long distance physical quantities [14]. We expect that this gives negligible effects on the short distance physics considered in this work. 3