In the traditional flow-resistance-differential (FRD) type valve-less piezoelectric pump,the generated outflow and pressure are discontinuous because of the inherent periodicity and fluctuation of the pump.To overcome these drawbacks,utilizing the bending vibration of piezoelectric bimorph to drive fluid was conducted.However,our investigation on the current status of this piezoelectric bimorph pump shows that larger driving force and vibration amplitude are required for fluid pumping; the pumping can be realized through the centrifugal force; and the mechanism of fluid pumping is no longer further studied.Based on these cases,the paper designed a piezoelectric-stack pump with variable-cross-section oscillating (VCSO) vibrator by imitating the swing of the caudal-fin of tuna,and the pump is neither the rotating type nor the volumetric type according to the taxonomy.The interaction between the oscillating vibrator and the fluid parcel is firstly analyzed from the viewpoint of momentum conservation,and the analytical expression of pump flow rate is obtained.Then the modal and harmonic response analyses on the vibrator immerged in water are carried out.From the analyses the first two orders resonance frequencies are 832 Hz and 1 939 Hz,respectively,and the peak value of the tip amplitude is 0.6 mm.Laser Doppler vibrometer is used to measure both the frequency and vibration amplitude,and the determined first two orders resonance frequencies are 617 Hz and 1 356 Hz,respectively.The measured tip amplitude reaches to the peak value of 0.3 mm.At last,experimental measurement for the flow rates with different driving frequencies is conducted.The results show that the flow rate can reach 560 mL/min at 1 370 Hz when the pump runs under the backpressure of 30 mm water column.And the flow rate is as much as 560％ of that of experiment results carried out by researchers from Brazil.The proposed pump innovates in both theory and taxonomy; in addition,the pump overcomes the drawbacks such as large flow fluctuation and low flow rate in the traditional FRD type pumps,which will help to broaden the application of the valve-less piezoelectric pump.