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In this paper, we proposed a ferrimagnetic mixed-spin (1, 3/2) Ising model to describe the ladder-like graphene nanoribbon. Using the Monte Carlo simulation, the effects of the anisotropies, exchange couplings, longitudinal magnetic field and temperature on the magnetic and thermodynamic properties were investigated. Typical temperature dependences of thermodynamics quantities such as magnetization, susceptibility and internal energy were presented under the influence of various physical parameters. The phase diagrams of blocking temperature were obtained in the different parameter planes. In particular, we also found some interesting double hysteresis loops behavior for certain physical parameters. Our results are consistent with those obtained by some theoretical and experimental researches. • The ferrimagnetic mixed-spin (1, 3/2) Ising ladder-like graphene nanoribbon in the longitudinal magnetic field has been studied. • Magnetization, susceptibility and internal energy have been discussed. • The phase diagrams of the blocking temperature under the influence of different parameters have been obtained. • The double hysteresis loops behavior has been found for certain physical parameters. [ABSTRACT FROM AUTHOR]