The objective of this paper is to investigate the space-time frequency spectra for cavitating flows in a mixed-flow pump by using both fast Fourier transform and wavelet transform. Unsteady cavitating flows in a mixed-flow pump are numerically investigated by using the Reynolds-averaged Navier-Stokes method, which is closured with SST k-ω turbulence model and Zwart cavitation model. The cavitation performance is fairly predicted when compared with available experimental data. There are two stages for unsteady cavitation evolution during one impeller rotating cycle, including the cavity growth stage and diminution stage. The cavitation in the impeller is characterized by the spatial non-uniform distribution since a high-pressure region presents at the impeller inlet plane. The pressure amplitude decreases when the cavitation becomes severer at a smaller operating velocity. Besides, the dominant frequency in the impeller is the impeller rotating frequency (fn), i.e. the cavity evolution frequency. Due to the rotor-stator interaction from the six-blade impeller, there is a dominant long-term frequency of 6fn in the intake duct and the diffuser inlet. Furthermore, a broadband low-frequency around 1.5fn exhibits near the diffuser exit, and the 1.5fn amplitude varies over time corresponding to different corner-vortex dynamics. Therefore, wavelet analysis is a more favorable and practical method to obtain time-dependent frequency information for unsteady cavitating flows.