The six-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 less than or equal to L less than or equal to 10. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical temperature are computed to be 3.00(12) and 1.47(10) using 6 less than or equal to L less than or equal to 10, respectively, which are in very good agreement with the theoretical predictions of 6/2 and a. The critical temperature for the infinite lattice is found to be 10.835(5) using 4 less than or equal to L less than or equal to 10 which is also in very good agreement with the precise results. The finite-size scaling relation fur the magnetic susceptibility at the infinite-lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite-size lattices. The finite-size scaling plots of the magnetic susceptibility and the order parameter verify the finite-size scaling relations about the infinite-lattice critical temperature. (C) 2000 Elsevier Science B.V. All rights reserved.