In semiconducting solar-cell absorbers, high absorption coefficient (alpha) near the band-edge region is critical to maximize the photocurrent generation and collection. Nevertheless, despite the importance of the band-edge absorption characteristics, the quantitative analysis of the band-edge optical transitions has not been performed. In this study, we have implemented systematic density functional theory (DFT) calculation, focusing on the band-edge oscillator strength of seven practical solar cell absorbers (GaAs, InP, CdTe, CuInSe2, CuGaSe2, Cu2ZnSnSe4, and Cu2ZnSnS4) with zincblende, chalcopyrite and kesterite structures. We find that all these crystals exhibit the giant oscillator strength near the band gap region, revealing the fact that alpha in the band gap region is enhanced significantly by the anomalous high oscillator strength. In high-energy optical transitions, however, the oscillator strength reduces sharply and the absorption properties are determined primarily by the joint density-of-state contribution. Based on DFT results, we show that the giant oscillator strength in the band edge region originates from a unique tetrahedral-bonding structure, with a negligible effect of constituent atoms.