The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($$ \ell = \frac{I} {J} $$) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δχ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $$ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $$ for $$ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $$ and $$ h = \frac{H} {J} = 0 $$ parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δℓ are in good agreement with the universal value (δh = 5) of the external magnetic field.