Based on the Monte Carlo simulation, research has been conducted on the magnetic and thermodynamic behaviors of a ferrimagnetic mixed-spin (5/2, 1/2) L10 nanoisland with a like quadrangular frustum pyramid structure. We studied the effects of the magneto-crystal anisotropy and exchange coupling on the magnetization, susceptibility, internal energy, and hysteresis loops. The ferrimagnetic system exhibits more abundant magnetic and thermodynamic behavior than the cubic L10 nanoisland. We found eight saturation values of magnetization, five-loop hysteresis loops, and abrupt transitions in the low-temperature region. In addition, the exchange coupling effect of ferrimagnetism also promotes magnetic properties. Interestingly, in this system, the ferromagnetic exchange coupling (Jaa) and external magnetic field (h) linearly depend on the blocking temperature TB. The hysteresis loops of the system have more magnetization steps, which reflects that it has more ground state spin configurations.