Comparison of high accuracy calculations with precision measurement of the 413 nm tune-out wavelength of the He(2 ^3S_1) state provides a unique test of quantum electro-dynamic (QED). We perform large-scale relativistic-configuration-interaction (RCI) calculations of the tune-out wavelength, that include the mass-shift operator, and fully account for leading relativistic nuclear recoil terms in the Dirac-Coulomb-Breit (DCB) Hamiltonian. We obtain the QED correction to the tune-out wavelength

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... ng perturbation theory, and the effect of finite nuclear size is also evaluated. The resulting tune-out wavelengths for the 2 ^3S_1(M_J=0) and 2 ^3S_1(M_J=± 1) states are 413.084 26(4) nm and 413.090 15(4) nm, respectively. Compared with the only current experimental value of 413.0938(9stat)(20syst) nm for the 2 ^3S_1(M_J=± 1) state, there is 1.8σ discrepancy between present theoretical work and experiment, which stimulates further theoretical and higher-precision experimental investigations on the 413 nm tune-out wavelength. In addition, we also determine the QED correction for the static dipole polarizability of the He(2 ^3S_1) state to be 22.5 ppm, which may enable a new test of QED in the future.