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We applied Monte Carlo simulation to investigate the thermodynamic properties and hysteresis loops of the hexagonal core-shell nanoparticle described by a ferrimagnetic mixed-spin (3/2, 5/2) Ising model. The results revealed the significance of the single-ion anisotropy, exchange coupling, external magnetic field in dominating various thermodynamic quantities and hysteresis loops. We obtained the variation of the critical temperature with various parameters. Under certain parameter conditions, the system may exhibit rich multiple-loop hysteresis behaviors, depending on the competition among the physical parameters. An Ising model of nanoparticle with hexagonal core-shell structure is proposed. The multiple profiles and saturation values of the magnetization are discovered in the system. [Display omitted] • A ferrimagnetic hexagonal core-shell nanoparticle was proposed under an external magnetic field. • Magnetization, susceptibility, and internal energy were discussed by Monte Carlo simulation. • The compensation temperature was found under the effect of single-ion anisotropy. • Multiple-loop hysteresis behaviors were discovered due to the competition among different physical parameters. [ABSTRACT FROM AUTHOR]