A compressed air supply system includes: a bleed air passage; an auxiliary compressor structure including a compressor inlet and a compressor outlet, the compressor inlet being fluidly connected to the bleed air passage; a supply passage which is fluidly connected to the compressor outlet and through which compressed air from the auxiliary compressor structure is supplied to an air cycle machine; an accessory gear box; and a continuously variable transmission structure that changes speed of rotational driving force output from the accessory gear box and rotates the auxiliary compressor structure. The continuously variable transmission structure and the auxiliary compressor structure are fixed to the accessory gear box, and the accessory gear box is fixed to the gas turbine engine.