The Ising models in seven and eight dimensions are simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4 <= L <= 8. Three different finite-size exponents for the order parameter near the curie point are computed to be 1.74 (3), 0.95 (2), 2.42 (5), 1.99 (19), 0.96 (1) and 2.95 (11) for d = 7 and d = 8 dimensions, respectively. The obtained results are in good agreement with the theoretical predictions, 7/4, 1, 5/2, 2, 1, 3 for d = 7 and 8 dimensions, respectively. The exponent in the finite-size scaling relation for the magnetic suscebtibility at the infinite-lattice critical temperature is computed to be 4.03 (9) using 4 <= L <= 8, which is in very good agreement with the theoretical prediction of 4 for d = 8 dimension. The finite-size scaling relation for 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 order parameter and the magnetic susceptibility verify the finite-size scaling relations about the infinite-lattice critical temperature. (c) 2005 Elsevier B.V. All rights reserved.