Unsteady cavitation flows in a centrifugal pump operating under off-design conditions are investigated by using a numerical framework combining the re-normalization group k–ɛ turbulence model and the transport equation-based cavitation model. The reliability and accuracy of the numerical model are demonstrated by the satisfactory agreement between the experimental and numerical values of the pump performance. Under partial discharge, the frequency spectra of the pressure fluctuation at the impeller inlet become more complex as the pump inlet pressure decreases. The maximum amplitude of pressure fluctuation at the blade leading edge for cavitation flow is 2.54 times larger than that for non-cavitation flow because of the violent disturbances caused by cavitation shedding and explosion. Under large discharge, the magnification on the maximum pressure amplitude is 1.6. This finding indicates that cavitation has less influence on pressure fluctuations in the impeller under large discharge than under partial discharge. This numerical simulation demonstrates the evolution of cavitation structure inside the impeller.