The six-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 <=, L <= 12. The exponents in the finite-size scaling relations for the magnetic susceptibility, the order parameter and the specific heat at the infinite-lattice critical temperature are computed to be 3.00(12), 1.49(12) and 0.001 (68) using 4 <= L <= 10, respectively, which are in very good agreement with the theoretical predictions of 6/2, 6/4 and 0. The critical temperature for the infinite lattice is found to be 10.8347(52) using 6 <= L <=, 12 which is also in very good agreement with the precise results. The finite-size scaling relation for magnetic susceptibility at the infinite-lattice critical temperature is also valid for the maxima of magnetic susceptibilities of the finite-size lattices. The finite-size scaling plots of magnetic susceptibility, the order parameter and the specific heat verify the finite-size scaling relations about the infinite-lattices temperature. (c) 2004 Elsevier Inc. All rights reserved.