The cooling fan is one of the important noise sources for new energy vehicles, and the research on its aerodynamic and aeroacoustic characteristics is of great help to improve the noise, vibration and harshness performance of new energy vehicles. However, most of these studies focus on the impeller, and little consideration has been given to the study of the shroud. Based on the coupling calculation method of large eddy simulation and the Ffowcs-Williams and Hawkings acoustics model, the aerodynamic and aeroacoustic characteristics in a cooling fan with the shroud are investigated at flow rates from 0.623 kg/s to 1.019 kg/s (where 0.865 kg/s is the flow rate corresponding to the best efficiency point). The accuracy of numerical simulation results is verified by the grid independence verification and the comparison of experimental data. Research shows that several large-scale vortex structures are observed in the clearance between the impeller and the shroud. The maximum peak-to-peak values of pressure fluctuation at different flow rates occur in the intermediate section or outlet section of the shroud. Although the shroud contributes relatively less to the far field noise, its different distribution may change the position of the maximum sound pressure level. The dominant frequency of pressure fluctuation equals the blade passage frequency (BPF) and the maximum SPL is around the BPF, both of which are independent of flow rates. The maximum SPL and the amplitude of the dominant frequency decrease as the flow rate increases.