This paper researches how to improve the performance and applications of micromixers used in mixing micro-liquids, because most of the existing micromixers need external power sources, and can only mix fluids but can not transport them. A valveless piezoelectric pump with multistage Y-shape tubes which integrates both functions of mixing and transporting is developed to overcome above shortcomings. Firstly, a multistage Y-shape tube is proposed, then a valveless piezoelectric pump with multistage Y-shape tubes is designed and its working principle is analyzed. Furthermore, the flow resistance characteristics and the flow rate of the valveless piezoelectric pump are analyzed theoretically. Meanwhile, finite element software is employed in simulating the flow fields of the pump numerically. The results show that the piezoelectric pump has a function of one-way transmission. Finally, the valveless piezoelectric pump is fabricated, the relationships between flow rate and driving frequency, as well as that between back pressure and driving frequency are experimentally investigated. The experimental results show that the maximum flow rate is 16.2 mL/min under a peak-to-peak voltage of power supply in 100 V(16 Hz), and the maximum back pressure is obout 64 mmH2O under a peak-to-peak voltage of power supply in 100 V (14 Hz). The obtained experimental results validate the feasibility of the valveless piezoelectric pump with multistage Y-shape tubes.