A gas compression system is provided. The gas compression system includes a compressor, an adsorption device, and a fluid control device. The compressor includes a first port and a second port. The adsorption device is adapted to output the high pressure hydrogen gas to the first port and absorb the low pressure hydrogen gas from the second port. The adsportion includes a first container connected to the first port or the second port, and a second container connected to the first port or the second port. The first container and the second container includes a hydrogen adsorption material adapted to release the high pressure hydrogen gas when heated, and absorb the low pressure hydrogen gas when cooled. A method of using the gas compression system is also provided.