The unsteady non-cavitation and cavitation turbulent flows in a centrifugal pump at partial load condition are numerically investigated by CFX 13.0. The numerical framework employs the combination of RNG k-ε turbulence model and transport equation cavitation model, in which the effects of compressibility of fluid on cavitation region and pressure fluctuation on saturation pressure are both taken into consideration. The good agreement between the numerical and experimental values validates that the numerical framework can accurately predict the turbulent flows in the centrifugal pump. The complex flow characteristics in impeller at non-cavitation and cavitation conditions are revealed. For the noncavitation flow, the dominant frequencies of pressure fluctuation of monitoring points in impeller are all the Impeller Rotation Frequency 24.17Hz. The maximum value of pressure fluctuation on the blade pressure side appears at the 0.8 chord length from the blade leading edge due to a clockwise rotating vortex, which incepts, develops and disappears when the corresponding blade passes through the volute tongue. The dominant frequencies of pressure fluctuation of monitoring points in volute are the Blade Pass Frequency 145 Hz or twice of it. The maximum value of pressure fluctuation in the volute appears near the tongue region, where the flow fields are uneven with strong second flow in the cross section. For the cavitation flow, as the cavitation develops at the blade leading edge, the turbulent flows in the impeller are greatly influenced by the bubble shedding and collapse. The maximum values of pressure fluctuation in impeller increase with the development of cavitation, and reach the largest magnification of about 2.0 in comparison to the non-cavitation flow when the pressure at the pump inlet is very low. The complicated phenomenon of unsteady turbulent flow in a centrifugal pump indicates that the vortex has great influence on the flow pattern.