Positron annihilation spectroscopy (PAS) is a sensitive probe of the shallow traps of light charged particles such as He/H embedded in solids. The nature of the shallow traps that attract positrons–i.e., whether the properties of the light charged particles or the number of particles contained in the traps affects the probability of positron capture–has so far remained unresolved. Here, the shallow traps of positron in FeCr alloy, namely (H, He)–V nano-clusters with open volume, have been investigated by first-principles calculations and a multi-grid based program package for electronic structure calculations. Various defect structures were modeled, including vacancies, interstitial helium atoms, and helium or hydrogen atoms occupying Fe vacancy sites. We calculated the charge density distribution at the (H, He)–V nano-clusters, and the results show that the charge density at the He/H–V clusters is significantly lower than around the neighboring Fe/Cr sites. The calculated lifetimes of positrons confined in the shallow traps are consistent with the effective open volume of the (H, He)–V complexes. These results suggest that a helium atom forms a more repulsive ion core than a hydrogen atom when it occupies the vacancy, resulting in a decrease in positron lifetime.