This study describes the large eddy simulations of a centrifugal pump impeller considering a sinusoidal flow rate and a constant rotation speed. Five different oscillation amplitudes of flow rate (A = 0.1Qd, 0.15Qd, 0.2Qd, 0.25Qd, and 0.3Qd, Qd indicates the design flow rate) are selected to determine the influence of oscillation amplitude on the internal flow characteristics. The simulation results show that, with increasing oscillation amplitude, the alternating stall phenomenon weakens or even disappears during the dropping stage, whereas the opposite trend is observed during the rising stage. The total mean normal vorticity is insensitive to changes in the oscillation amplitude. Moreover, the difference in pressure fluctuations between adjacent passages decreases with increasing oscillation amplitude. The first and second dominant frequencies of the pressure fluctuations are mainly affected by the oscillation amplitude in the non-stall passage. The internal flow exhibits a clear hysteresis effect, and the lag time of the head increases with the oscillation amplitude. Additionally, the average head is approximately 2.38 m, regardless of the oscillation amplitude.