The present invention relates to a multistage fluid compressor including a motor housing having a fluid injection port, a stator coupled to the inside of the motor housing, a rotor configured to penetrate the inside of the stator and having two opposite sides based on an axial direction, the two opposite sides being rotatably coupled to the motor housing, an impeller housing coupled to the motor housing and configured to communicate with the inside of the motor housing, the impeller housing having a fluid discharge port configured to connect the inside and outside thereof, and first and second impellers provided in the impeller housing and coupled to one end of the rotor, in which the compressor may be directly cooled by using a fluid intended to be compressed, and components of the compressor including a thrust bearing, the stator, and the rotor may be efficiently cooled.