We report on a class of quantum spin Hall insulators (QSHIs) in strained-layer InAs / GaInSb quantum wells, in which the bulk gaps are enhanced up to fivefold as compared to the binary InAs / GaSb QSHI. Remarkably, with consequently increasing edge velocity, the edge conductance at zero and applied magnetic fields manifests time reversal symmetry-protected properties consistent with the Z 2 topological insulator. The InAs / GaInSb bilayers offer a much sought-after platform for future studies and applications of the QSHI.