The development of organ-on-a-chip systems demands high requirements for adequate micro-pump performance, which needs excellent performance and effective transport of active cells. In this study, we designed a piezoelectric pump with a flexible venous valve inspired by that of humans. Performance test of the proposed pump with deionized water as the transmission medium shows a maximum output flow rate of 14.95 mL/min when the input voltage is 100 V, and the pump can transfer aqueous solutions of glycerol with a viscosity of 10.8 mPa·s. Cell survival rate can reach 97.22% with a yeast cell culture solution as the transmission medium. A computational model of the electric-solid-liquid multi-physical field coupling of the piezoelectric pump with a flexible venous valve is established, and simulation results are consistent with experimental results. The proposed pump can help to construct the circulating organ-on-a-chip system, and the simple structure and portable application can enrich the design of microfluidic systems. In addition, the multi-physical field coupling computational model established for the proposed piezoelectric pump can provide an in-depth study of the characteristics of the flow field, facilitating the optimal design of the micro-pump and providing a reference for the further study of active cell transport in organ-on-a-chip systems.