This paper mainly investigates the vibration characteristics of piezoelectric pipe conveying fluid subjected to fluid-structure-electrical interaction. Based on the Hamilton’s principle, the dynamic equations of the cantilever piezoelectric pipe subjected to the weight and fluid-structure-electrical interaction are established and solved by using the Galerkin method. Ultimately, complex frequency and critical flow velocity are obtained. The main discussion focused on the influence of electromechanical coupling, resistive load, and dimensionless capacitance on the critical flow velocity under different lengths of piezoelectric materials. It also examined the dynamic trajectories of the real and imaginary parts of the complex frequency under various mass ratios and resistive loads. Furthermore, it explored the impact of parameters representing voltage on the stability of the system. The results indicate various stability evolutions under different lengths of piezoelectric materials, flow velocities, and parameters representing voltage. The stability of the system pipe is influenced by factors such as the length of the piezoelectric material and resistive load.