For the centrifugal pump, the rotor−stator interaction (RSI) induces high-energy pressure pulsation, which directly affects the stability of systems and equipment. Therefore, this work proposes a new staggered impeller structure to suppress high-energy pressure pulsation in centrifugal pumps. The original impeller blade is divided into two layers and is staggered at 10°, 20° and 30° to form a staggered impeller. The dynamic pressure pulsation characteristics of both the original impeller and the staggered impeller are predicted using large eddy simulation (LES). The results indicate that the uniform staggered arrangement of blades can significantly reduce the pressure pulsation energy in the pump by 54.69% under the design conditions, while also achieving the best performance. Even under off-design conditions, the pressure pulsation energy can still be effectively suppressed by the staggered blades. The study of the time−frequency domain of the monitoring points near the tongue found that the phase difference in the pressure fluctuation caused by the RSI between the staggered impeller and the tongue prevents the superposition of pressure pulsation energy and efficiently suppresses it in the pump. The results can provide a reference for optimizing low-vibration-noise pump impellers in engineering applications.