A quantum simulation approach facilitated by the self-consistent algorithm was applied in the present work to ferromagnetic and antiferromagnetic three-dimensional Heisenberg lattices consisting of S = 1 spins. Consequently, the calculated spontaneous magnetizations for the two sorts of lattices are precisely consistent with mean-field theory in the whole temperature range. Especially, the numerical results, such as magnetizations, total energies and total free energies per mole of spins, show no size effects. Thus, the physical properties of a huge bulk magnet can be estimated by performing simulation for a very tiny sample, so that the computational time can be greatly saved.