In this paper, a streamlined flow tube valveless piezoelectric pump (SLFT PZT pump) is proposed to modify the single flow trend and improve the fluid flow stability. Firstly, the structural and working principle of the streamlined flow tube, which accounts for changing the flow trend and improving the flow stability, were analyzed. The flow resistance and flow rate equations were established. Secondly, the pressure and velocity fields of the tube were simulated. These simulated results were consistent with the theoretical results. Thirdly, the flow resistance of the flow tube was tested with pressure differences of 1000 Pa, 1200 Pa, 1400 Pa and 1600 Pa respectively. The trend of the result curves was consistent with the simulated results. The amplitude-frequency relationship and the flow-rate-frequency relationship were also tested, both result curves highly corelate. The maximum amplitude was 0.228 mm (10 Hz, 120 V), and the maximum flow rate was 17.01 mL/min (10 Hz, 100 V). Finally, the theoretical flow rate of the SLFT PZT pump was calculated at 100 V and 120 V. These results roughly fitted with the experimental results. The streamlined flow tube could change the internal flow trend that remarkably improved the flow stability. Therefore, it promoted the application of the valveless PZT pump in living cells, biomedical and polymer delivery.