To provide a comprehensive understanding of the pressure fluctuation-vortex interaction in non-cavitation and cavitation flow, in this article, the unsteady flow in an ultra-low specific-speed centrifugal pump was investigated by numerical simulation. The uncertainty of the numerical framework with three sets of successively refined mesh was verified and validated by a level of 1% of the experimental results. Then, the unsteady results indicate that the features of the internal flow and the pressure fluctuation were accurately captured in accordance with the closed-loop experimental results. The detailed pressure fluctuation at 16 monitoring points and the monitoring of the vorticity suggest that some inconsistent transient phenomena in frequency spectrums show strong correlation with the evolution of vortex, such as abnormal increasing amplitudes at the monitoring points near to the leading edge on the suction surface and the trailing edge on the pressure surface in the case of lower pressurization capacity of impeller after cavitation. Further analysis applies the relative vortex transport equation to intuitionally illustrate the pressure fluctuation-vortex interaction by the contribution of baroclinic torque, viscous diffusion and vortex convection terms. It reveals that the effect of viscous diffusion is weak when the Reynolds number is much greater than 1. Pressure fluctuation amplitude enlarges on the suction side of blade near to the leading edge due to the baroclinic torque in cavitation regions, whereas the abnormal increase of pressure fluctuation after cavitation on the pressure surface of blade approaching the trailing edge results from the vortex convection during vortices moving downstream with the decrease of available net positive suction head at the same instance.