Valveless piezoelectric pump with multistage Y-shape tubes has the function of micro-mixing, but it exists the problem of unbalance between the output flow and the output capacity of the piezoelectric vibrator. So, a valveless piezoelectric pump with asymmetrical bifurcated channels is proposed in this paper. First, the relationship between flow resistance and output flow of the valveless piezoelectric pump is obtained through theoretical analysis. Then, the flow resistance of the multistage Y-shape tube is numerically calculated by using finite element software. Finally, the prototype is fabricated by stereolithography technology, and performance experiments of the piezoelectric pump and vibration of the piezoelectric vibrator are performed. Experimental results show that the flow rate, head and amplitude of piezoelectric vibrator increase first and then decrease with the increase of driving frequency when the piezoelectric pump is driven with a sinusoidal voltage of 200Vpp. The maximum flow rate of 4g/min is obtained at 31Hz and the pump head can reach a maximum of 40.5mmH2O at 38Hz. The output performance of the pump is positively correlated with the driving voltage of the piezoelectric vibrator. The proposed valveless piezoelectric pump has a bifurcated channel and thus suitable for microfluidic drip irrigation and mixing applications. The study validates the feasibility of the valveless piezoelectric pump with asymmetrical bifurcated channels and provides a reference for the application in micro-channel drip irrigation and micro-mixing fields.