The vibration induced by the unsteady fluid exciting force in a centrifugal pump is one of the important factors affecting the reliable operation of the pump. In this study, the cutting of the blade trailing edge of a straight blade is presented to improve the unstable flow and vibration in a centrifugal pump. Based on the large eddy simulation (LES) and fluid–solid coupling method, the transient pressure pulsation, unstable flow structure, and vibration displacement of a centrifugal pump were investigated with different cutting angles of the trailing edge under the design flow rate. The external characteristics of the centrifugal pumps were calculated and compared using the shear stress transport (SST) k–ω turbulence model. The results show that the heads and efficiencies of the pumps with 30 deg and 45 deg cutting angles of the trailing edge slightly improved. The pressure pulsation on the volute evaluated by dominant frequency–amplitude and pressure pulsation energy was reduced due to the lesser average vorticity intensity and trailing vortex area in the centrifugal pump. Therefore, the vibration displacement and the vibration energy at the low frequency of the impeller decreased.