To provide a multistage booster effectively cooling an inside of a crank case.

This device is provided with a low pressure side communication pipe 18a leading gas boosted by a low pressure side cylinder 7L into an inside of a hermetic crank case 8 provided with a crankshaft 11 making pistons 9L, 9H reciprocate in each cylinder 7L, 7H, and a high pressure communication pipe 18b leading gas introduced to the inside of the crank case 8 to an inside of a high pressure side cylinder 7H. A cooler 19 cooling gas boosted by the low pressure side cylinder 7L is provided in the low pressure side communication pipe 18a. The gas boosted by the low pressure side cylinder 19 is sent to the inside of the high pressure side cylinder 7 via the inside of the crank case after cooled by the cooler 19.