In this study, the blade shape of the squirrel-cage fan system inside the range hood was optimized using the surrogate model to improve the maximum volume flow rate. The influence of computational fluid dynamics (CFD) noise was concerned. The regression Kriging model (RKM) was used as a surrogate model to reflect the relationship between the design parameters of the blade and the volume flow rate. The parallel filling criterion after re-interpolation was used to improve the optimization efficiency further and ensure global optimization. Through experimental verification, we found that the relative error between the volume flow rate of the optimal sample of RKM and the experiment was only 0.4%. Compared with the prototype, the maximum volume flow rate of the optimal sample of RKM was increased by 2.9%, and the efficiency under the corresponding working conditions was increased by 2%. RKM was used to predict the velocity field of the volute and impeller exit section to explore the feasibility of the RKM in the flow field prediction. Research shows that the RKM cannot accurately predict the velocity of each grid on the cross-section. Still, it can accurately predict the changing trend of the velocity.