Nanographite systems, where graphene sheets of the orders of the nanometer size are stacked, show novel magnetic properties, such as, spin-glass like behaviors and the change of ESR line widths in the course of gas adsorptions. We theoretically investigate stacking effects in the zigzag nanographite sheets by using a tight binding model with the Hubbard-like onsite interactions. We find a remarkable difference in the magnetic properties between the simple A-A and A-B type stackings. For the simple stacking, there are not 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. Relations with experiments are discussed.