Catalyzes the reduction of hydroperoxides in a glutathione- dependent manner thus regulating cellular redox homeostasis (PubMed:36608588, PubMed:8428933). Can reduce small soluble hydroperoxides such as H2O2, cumene hydroperoxide and tert-butyl hydroperoxide, as well as several fatty acid-derived hydroperoxides (PubMed:36608588, PubMed:8428933). Cannot reduce phosphatidycholine hydroperoxide (PubMed:8428933). {ECO:0000269|PubMed:36608588, ECO:0000269|PubMed:8428933}. This is the function of ENSG00000176153 (GPX2, glutathione peroxidase 2).