Protects cells and enzymes from oxidative damage, by catalyzing the reduction of hydrogen peroxide, lipid peroxides and organic hydroperoxide, by glutathione. May constitute a glutathione peroxidase-like protective system against peroxide damage in sperm membrane lipids. 2 glutathione + H2O2 = glutathione disulfide + 2 H2O Epididymis. Belongs to the glutathione peroxidase family.