In the field of the pumped storage plants, the unstable flow is universally caused by the rotating stall in the hydro-energy machinery, which further deteriorates the performance curves. To explore the alleviation method of the unstable flow, flow characteristic in a centrifugal pump with different impeller blade geometries is numerically investigated using a modified SST k-ω partially averaged Navier-Stokes model in this study. Numerical validation on the characteristic curves is carried out, which appears in accord with the experimental data of the test pump. Four types of available modification methods are attempted based on theoretical analysis, i.e., trimming the section side of the blade at trailing edge (TE) (named model A), decreasing the blade angle at TE (named model B), trimming the blade TE in spanwise direction with 45 degree (named model C) and adopting large lean angle blades (named model D). Results on the characteristic curves are first compared. In the test pump and model B, one positive slope region is observed under the same operation condition, while it is brought forward in the model A. On the contrary, the positive slope region is completely alleviated in model C and model D. Further exploration on the flow pattern in the impeller is conducted to give a comprehensive explanation. Due to the sudden increment of the energy loss, the flow pattern tends to be deteriorated, which further has impact on the characteristic curves. At last, unstable flow analysis in the impeller of the model D is carried out with emphasis on the evolution of the rotating stall. By using large lean angle blades, the rotating stall in the blade-to-blade passage of impeller is alleviated significantly with lower pressure fluctuation intensity.