Imitating the structure of the venous valve and its characteristics of passive opening and closing with changes in heart pressure, a piezoelectric pump with flexible valves (PPFV) was designed. Firstly, the structure and the working principle of the PPFV were introduced. Then, the flexible valve, the main functional component of the pump, was analyzed theoretically. Finally, an experimental prototype was manufactured and its performance was tested. The research proves that the PPFV can achieve a smooth transition between valved and valveless by only changing the driving signal of the piezoelectric (PZT) vibrator. The results demonstrate that when the driving voltage is 100 V and the frequency is 25 Hz, the experimental flow rate of the PPFV is about 119.61 mL/min, and the output pressure is about 6.16 kPa. This kind of pump can realize the reciprocal conversion of a large flow rate, high output pressure, and a small flow rate, low output pressure under the electronic control signal. Therefore, it can be utilized for fluid transport and pressure transmission at both the macro-level and the micro-level, which belongs to the macro–micro combined component.