The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 4, 6, 8, 10. The temperature variations and the finite-size scaling plots of the specific heat and Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T-C = 10.838(1), T-C=10.836(20) and T-C=10.835(l) are obtained from the intersection points of specific heat curves, Binder parameter curves and the straight line fit of specific heat maxima, respectively. These results are in agreement with the more precise value of T-C=10.835(5). The value obtained for the critical exponent of the specific heat, i.e., alpha = 0.012(2) is also in agreement with alpha = 0 predicted by the theory. (C) 2004 Elsevier B.V. All rights reserved.