The magnetic properties of an Ising antiferromagnetic model on a nanographene lattice which have spins that can take the values S = ±3/2, ±1/2, are studied by Monte Carlo simulations. We only consider the nearest-neighbor interactions between the sites i and j . The zero field cooled and field cooled magnetizations, magnetic susceptibilities and hysteresis cycle are obtained for a nanographene structure with the effect of exchange interaction between sites i and j . The blocking temperature is also obtained for specific values of the external magnetic field.