Flow instability and its correlations with performance characteristics were investigated for a centrifugal pump with a volute. Unsteady three-dimensional Reynolds-averaged Navier–Stokes analysis was performed to analyze the flow and performance characteristics using the shear stress transport (SST) turbulence model. The grid dependence and temporal resolution were tested to evaluate the numerical uncertainties, and the numerical solutions were validated using experimental data. The total-to-static head coefficient, the impeller's total-to-static head coefficient, and the volute static pressure recovery coefficient were selected as performance parameters. To identify the flow instability, pressure fluctuations were monitored upstream of the impeller, at the volute inlet, and on the shroud wall of the impeller. Three different types of flow instability were detected in partial-load conditions: inside the volute, upstream of the impeller, and at the interface between the impeller and volute. The time-dependent flow structures were investigated to obtain insight into the onset of the flow instability. The correlation of the onset of the flow instability with the performance curves was discussed.