Using the Monte Carlo simulation, research has been implemented on the magnetic and thermodynamic behaviors of a ferromagnetic mixed-spin (3/2, 1/2) L10 nanoisland with a layered face center cubic structure. The investigation was made on the effects of such aspects as anisotropies, exchange couplings, external magnetic field, and temperature on magnetization, susceptibility, internal energy, and hysteresis loop. Meanwhile, behavior of the hysteresis loop is demonstrated under the influence of the above physical parameters. In addition, triple saturation values, single hysteresis loops, and χ curve double peak are found in this system. The blocking temperature, hysteresis loop area, and coercivity increase linearly with the exchange coupling. Particularly, the high critical temperature and coercivity of this nanoisland depend on the exchange coupling(Jaa,Jab) and anisotropy(Da).