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We employed the effective-field theory with correlations to study the hysteresis and thermodynamic properties of a bilayer graphene-like ring with edge decorated by a ferrimagnetic mixed-spin (2, 5/2) Ising model. The temperature dependence of magnetization, susceptibility, internal energy and specific heat of the system are illustrated in detail. As well, we depict the hysteresis behaviors and phase diagram with various parameters. The results showed the significance of the anisotropy, the magnetic field as well as the exchange coupling in controlling hysteresis behaviors and various magnetic quantities. The possibility of rich multiple-loop hysteresis and reentrant behaviors are found, sensitive to the competition among the physical parameters.

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