A heat exchanger that can mechanically automatically control a level of cooling water according to heat generation of the fuel cell. The heat exchanger includes a housing having a cooling water inlet and an outlet connected to a fuel cell stack, a moving plate which moves reciprocally in the housing and discharges cooling water filled in the housing to the stack when it moves in a one direction and when it receives a steam pressure from the stack it moves in an opposite direction, and an elastic member that applies a force to the moving plate in the one direction. The heat exchanger can automatically maintain the level of cooling water despite a difference in heat generated between a full and a partial load operation of the fuel cell obviating complicated electronics such as a thermo-sensor, a valve, or a controller. Also, under a partial load, the exposure of flow channels to superheated steam is avoided, thereby extending the lifetime of the fuel cell.