The mixed spin 3-spin 3/2 ferrimagnetic Ising model was simulated using cooling algorithm on cellular automaton (CA). The simulations were carried out in the intervals -4 D-A/J 8 and -4 D-B/J 8 for the square lattices with periodic boundary conditions. The ground-state phase diagram of the model has different types of ferrimagnetic phases. Although only the antiferromagnetic nearest-neighbor interaction was contained in the Hamiltonian, the compensation points emerged through D-A/J = 2 at kT/J = 0. The values of the critical exponents (, , and ) were estimated within the framework of the finite-size scaling theory and power-law relations for the selected D-A/J values (-2, 0, 1, 2, and 4). The estimated critical exponent values were in good agreement with the universal values of the two-dimensional Ising model ( = 1, = = 0, = 0.125, = 0.875 and = = 1.75).