Quantum spin Hall insulators (QSHIs), also known as two-dimensional topological insulators, have emerged as an unconventional class of quantum states with insulating bulk and conducting edges originating from nontrivial inverted band structures and have been proposed as a platform for exploring spintronics applications and exotic quasiparticles related to the spin-helical edge modes. Despite theoretical proposals for various materials, however, experimental demonstrations of QSHIs have so far been limited to two systems—HgTe/CdTe and InAs/GaSb—both of which are lattice-matched semiconductor heterostructures. Here, we report transport measurements in yet another realization of a band-inverted heterostructure as a QSHI candidate—InAs/InxGa1−xSb with lattice mismatch. We show that the compressive strain in the InxGa1−xSb layer enhances the band overlap and energy gap. Consequently, high bulk resistivity, two orders of magnitude higher than for InAs/GaSb, is obtained deep in the band-inverted regime. The strain also enhances bulk Rashba spin-orbit splitting, leading to an unusual situation where the Fermi level crosses only one spin branch for electronlike and holelike bands over a wide density range. These properties make this system a promising platform for robust QSHIs with unique spin properties and demonstrate the strain to be an important ingredient for tuning spin-orbit interaction.