We optimized the shroud of an axial cooling fan in a mechanical room of a household refrigerator using the response surface method (RSM) based on numerical predictions in terms of high flow rate and low noise. Computational fluid dynamics (CFD) techniques and an acoustic analogy were used to predict the volume flow rate (VFR) and noise in the system. The numerical methods were validated by comparing their VFR and acoustic power level predictions with the measured data. Then, the RSM was used to optimize the design parameters of the shroud of an axial cooling fan. The numerical prediction using optimum design obtained for maximum VFR from the RSM showed that the VFR can be increased by 21.8% at the cost of an increase in the acoustic power level by 1 dB. The prediction for minimum noise reveals that the acoustic power level can be reduced by 3.55 dB at the same flow rate as the original model. The orifice length of the shroud and the serrated structure are found to contribute significantly to the flow rate and radiated noise, respectively. Physical reasons for these observations are given based on detailed investigations of the variations of flow fields due to the design parameters.