The magnetic properties and magnetocaloric effect of an antiferromagnetic/ferromagnetic (AFM/FM) BiFeO3/Co bilayer with mixed-spin (5/2, 3/2) have been studied based on Monte Carlo simulation. The magnetization, susceptibility, and critical temperature are investigated under various exchange couplings and an external magnetic field. In particular, the influence of exchange couplings and an external magnetic field on the magnetic entropy change, adiabatic temperature change, and the relative cooling power (RCP) are studied. The simulation results indicated that the decrease of the exchange coupling and the increase of external magnetic fields can cause an increase of magnetic entropy change, adiabatic temperature change, and RCP. In addition, the hysteresis loops of the system are presented for different exchange couplings and temperatures.