Abstract: In this work, we have performed Monte Carlo simulations to study a mixed spin-1 and spin-3/2 Ising ferrimagnetic system on a square lattice with two different random single-ion anisotropies. This lattice is divided in two interpenetrating sublattices with spins S-A = 1 in the sublattice A and S-B = 3/2 in the sublattice B. The exchange interaction between the spins on the sublattices is antiferromagnetic (J < 0). We used two random single-ion anisotropies, D-i(A) and D-j(B), on the sublattices A and B, respectively. We have determined the phase diagram of the model in the critical temperature T-c versus strength of the random single-ion anisotropy D plane and we shown that it exhibits only second-order phase transition lines. We also shown that this system displays compensation temperatures for some cases of the random single-ion distribution. (C) 2018 Elsevier B.V. All rights reserved.