We demonstrate stretchable amorphous indium-gallium-zinc-oxide (a-IGZO) thin-film transistors (TFTs) on polyimide (PI)/polydimethylsiloxane (PDMS). TFTs/PI island on the stretchable PDMS substrate maintain their electrical characteristics even after being stretched up to 20% strain. TFTs on PI/PDMS substrate exhibit robust electrical performances for stretchable devices.