A system for stacking fuel cells for a fuel cell stack includes, a component part storage region to store the fuel cells, a finished product storage region to store a completed fuel cell stack transferred by an automated guided vehicle, and a plurality of stacking regions disposed between the component part storage region and the finished product storage region, where a pair of stacking units are disposed at opposite sides of a first transfer robot that is centrally disposed in the stacking region, one side of the stacking region is formed as an entry and exit for the automated guided vehicle for the fuel cell stack, and the stacking region is supplied with the fuel cells from the component part storage region by the automated guided vehicle to sequentially stack the fuel cells to manufacture the fuel cell stack.