The spin-1 Ising model with the dipole-quadrupole interaction (l = L/J) has been simulated using a cellular automaton (CA) algorithm improved from the Creutz cellular automaton (CCA) for a face-centered cubic (fcc) lattice. The simulations have been made for different l values at the reentrant phase transition and the special points such as the tricritical point (k = K/J = 0, 0 = D/J = 5.7) and the critical end point (k = -0.9, d = 0.7). The simulation results show that the model has the dense ferromagnetic (df, df(+), df(-)) and the ferromagnetic (F, F(+), F(-)) phases with the dipole-quadrupole interaction. The type and the order of the phase transitions change for the nonzero values of k on the special points. Furthermore, the effect of is similar with the effect of the external magnetic field (h).