A compression apparatus includes an electrolyte membrane, an anode provided on a first principal surface of the electrolyte membrane, a cathode provided on a second principal surface of the electrolyte membrane, an anode separator provided on the anode, a cathode separator provided on the cathode, and a voltage applier that applies a voltage between the anode and the cathode. The compression apparatus causes, by using the voltage applier to apply a voltage, protons taken out from a hydrogen-containing gas that is supplied to the anode to move to the cathode via the electrolyte membrane and produces compressed hydrogen. The anode separator has a first flow channel, provided in a principal surface thereof facing away from the anode, through which a cooling fluid flows.