We present a numerical study based on Monte Carlo algorithm of the magnetic properties of a mixed Ising ferrimagnetic model on a cubic lattice where spins $sigma =pm 1/2$ and spins $S=0,pm 1$ are in alternating sites on the lattice. We carried out exact ground state calculations and employ a Monte Carlo simulation to obtain the finite-temperature phase diagram of the model. A compensation point appears when the next-nearest-neighbor interaction between the spins $sigma =pm 1/2$ exceeds a minimum value. We found a strong dependence of the compensation temperature with the interactions in the Hamiltonian, particulary the crystal field and the external field. An applied field can change the range of values of the compensation temperature from zero up to a maximum value that depends on the field.
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