The pumping and mixing performance of a valveless piezoelectric pump were proposed and studied. A hemisphere-segment group that was fixed in the pump played the role of a valve. Based on the theoretical analysis of the pumping performance, the changes of the fluid velocity field, pressure difference, the coefficient of resistance and flow rate were simulated with FLUENT. Simulation results revealed the relationships among the pressure field, flow rates, row and column numbers, and row and column intervals of the hemisphere-segment group. The simulation results indicated that increasing row and column numbers, increasing row intervals, and decreasing column intervals could all increase the flow resistance difference in pump flow field and thus increased the flow rate. It was also found that the pumping effect was significantly improved by increasing row number than increasing column number; the increasing of row and column intervals could increase the size and strength of the vortex, and then improve the mixing and stirring performance of this pump. Finally, simulation results were tested and verified through pump flow-rate experiments.