Unsteady pressure pulsation and fluid force induced by flow instabilities in the centrifugal pump is an important cause of vibration, which is detrimental to the safe operation of the pump. In this study, we numerically investigated the pressure pulsation and radial force in a low-specific-speed centrifugal pump by using the detached-eddy simulation method. We also performed a vibration displacement experiment on the shaft of the centrifugal pump. The vortex identification method was introduced to clarify the internal correlation between unsteady flow structures with pressure pulsations. The results showed that the pressure pulsations at the impeller outlet were closely associated with the periodic vortex shedding from the blade pressure surface. The rotor–stator interaction between a relatively big trailing vortex core and volute tongue generated larger pressure pulsation and radial force in the pump at a low flow rate. Under a large flow rate, the trailing vortex core was easily broken and dispersed, and this resulted in smaller pressure pulsation and radial force compared with that at a low flow rate. Under the design flow rate, the pressure pulsation intensity and the radial force in the impeller were smaller than that under the off-design flow rate. Compared with the spectra between the radial force on the impeller and radial displacement on the shaft, they both presented higher amplitude at the shaft frequency. The vibration of the pump shaft was closely related to the radial force on the impeller.