A hydrogen compression system includes an inner container made of a non-magnetic element and having a hydrogen inlet/outlet portion through which hydrogen flows in or out of the inner container, a metal hydride material accommodated in the inner container, an outer container configured to surround the inner container and having an inlet/outlet port through which hydrogen flows in or out of the outer container, and an induction heating unit disposed between the inner container and the outer container and configured to heat the metal hydride material by induction heating, thereby obtaining an advantageous effect of simplifying a structure and process for heating the metal hydride material and quickly heating the metal hydride material to an accurate temperature.