We propose a ternary Ising spins (1/2, 1, 3/2) model to investigate the thermal and magnetic properties of magnetic nanoparticles with core-shell structure within the framework of the effective-field theory with correlations. The center site of the core is occupied by sigma = +/- 1/2 spin, while those surrounding the center site are occupied by S = +/- 1, 0 spins and the shell sites are occupied by m = +/- 1/2, +/- 3/2 spins. Thermal behaviors of the core and shell magnetizations, susceptibilities and internal energies as well as total magnetization are examined. In order to confirm the stability of the solutions we also investigate the free energy of the system. According to the values of Hamiltonian parameters, the system undergoes first- and second-order phase transitions. Phase diagrams are calculated and discussed in detail. We find that the system exhibits a tricritical point, reentrant and five different type (Q, P. R, S and W) of compensation behaviors that strongly depend on interaction parameters. The results are in good agreement with some experimental and theoretical results. (C) 2013 Elsevier B.V. All rights reserved.