As an advanced finishing technology, magnetic compound fluid finishing (MCFF) is considered to be able to achieve damage-free finishing of low-hardness materials such as copper alloys with appropriate finishing parameters. However, ignoring the influence of the material removal amount on the dimensional accuracy when optimizing the finishing parameters may result in excessive material removal and a reduction in the workpiece's dimensional accuracy. Thus, a novel finishing parameters optimization method considering dimensional accuracy is proposed in this paper. Firstly, the MCFF experiments are planned and carried out for modeling. Secondly, a MCFF model is established based on the integrated learning theory. The established model is a multi-layer neural network fusion model comprised of a prediction layer and a fusion layer, which can accurately predict the polished surface quality and material removal amount. Thirdly, taking the effect of material removal amount on the dimensional accuracy into account, the finishing parameters are optimized by the multi-objective particle swarm optimization algorithm. Finally, the model's prediction accuracy and the superiority of the optimized parameters are compared and verified by experiments. The results demonstrate that the developed model can correctly predict the finishing effect, and the high-quality polished surfaces and high dimensional accuracy can be obtained with the optimized finishing parameters.