In this work, the magnetic properties of the ferromagnetic and antiferromagnetic two layer spin-1/2 Ising nanographene systems are investigated within the effective held theory. We find that the magnetizations and the hysteresis behaviors of the central graphene atoms are similar to those of the edge graphene atoms in the ferromagnetic case. But, they are quite different in the antiferromagnetic case. The antiferromagnetic central graphene atoms exhibit type II superconductivity and they have triple hysteresis loop. The peak effect (PE) region is observed on the hysteresis curves of the antiferromagnetic Ising nanographene system. Therefore, we suggest that there is a strong relationship between the antiferromagnetism and the peak effect. Our results are in agreement with some experimental works in recent literature. (C) 2014 Elsevier B.V. All rights reserved.