Nanographite systems show novel magnetic properties. We theoretically investigate stacking effects in the zigzag nanographite sheets to find a remarkable difference in the magnetic properties. For the simple stacking, there are no magnetic solutions. For the A-B stacking, we find antiferromagnetic solutions for strong onsite repulsions. The local magnetic moments tend to exist at the edge sites in each layer due to the large amplitude of wavefunctions at these sites. We study Variations between the A-A and A-B stackings, and find that the magnetism between the two stackings experiences the first-order phase transition.