Dynamic valveless piezoelectric pumps are widely used in the field of microfluidics due to their advantages such as ease of miniaturization, absence of pump valve hysteresis, and lack of fine tubing within the pump chamber. However, all currently known dynamic valveless piezoelectric pumps can only achieve unidirectional liquid pumping, which limits their ability to fully utilize their advantages in practical applications. This study draws inspiration from the tail structure of fish and innovatively designs a flexible fish-tail valveless piezoelectric pump. By setting a flexible structure at the tail of the piezoelectric vibrator, the vibration mode of the piezoelectric vibrator is altered, enabling the adjustment of liquid flow direction in the pump chamber under different excitation frequencies. Flow rate test results show that, at a voltage of 160 V, the maximum forward flow rate is 23.68 ml/min (105 Hz), and the maximum reverse flow rate is 5.76 ml/min (230 Hz). Doppler scanning laser vibrometry and flow field observation experiments were used to verify the relationship between the vibration mode changes of the flexible fish-tail piezoelectric vibrator and the flow direction deflection at high and low frequencies. This research provides a more flexible and efficient fluid control technology for applications such as microfluidic mixing, drug delivery, and biotechnology research.