A computational study based on the cellular automaton has been done to investigate the phase transition of the spin-3/2 Blume-Emery-Griffiths (BEG) model. In the study. the ferromagnetic spin-3/2 BEG model with repulsive biquadratic coupling is simulated by using the cooling algorithm improved from the Creutz cellular automaton (CC:A). The temperature dependence of the order parameters and associated fluctuations are calculated at various of the model parameters and the phase diagrams of the model are constructed in the (D/J, kT/J) and (K/J, kT/J) plane in the absence and presence of the external magnetic field. The phase diagrams of the model exhibit a rich variety of behaviors. It is shown that different kinds of phase transitions take place between the disordered, ferromagnetic, ferrimagnetic and antiquadrupolar phases for various of model parameters at a magnetic field value in the interval -0.06 <= h/J <= 0. In contrast. there is only a transition between disordered and ferrimagnetic phases in the interval -0.2 <= h/J< -0.06. Results are compared with other approximate methods.