This paper investigates the flexural wave propagation and control in a novel piezoelectric composite pipe conveying fluid. The pipe features dual periodic piezoelectric layers acting as sensors and actuators, connected by a feedback amplifying circuit, forming a self-powered phononic crystal (PC) control structure. The vibration reduction is actively tuned by adjusting the feedback control gain, rather than altering the pipe's construction. The pipe is made of functionally graded material (FGM) with continuously varying material properties along the radial direction and a poroelastic medium. Using Timoshenko beam theory and Hamilton’s principle, electromechanical coupling equations are derived to govern the flexural vibration. Spectral element technology is applied to analyze the band structure, band gap (BG) distribution, and frequency response. Parametric studies validate the excellent vibration control effect and highlight the significant impacts of material, piezoelectric layers, feedback control, and flowing fluid on BG characteristics. This research provides a technological reference for vibration and elastic wave control in engineering composite pipe structures.This paper investigates the flexural wave propagation and control in a novel piezoelectric composite pipe conveying fluid. The pipe features dual periodic piezoelectric layers acting as sensors and actuators, connected by a feedback amplifying circuit, forming a self-powered phononic crystal (PC) control structure. The vibration reduction is actively tuned by adjusting the feedback control gain, rather than altering the pipe's construction. The pipe is made of functionally graded material (FGM) with continuously varying material properties along the radial direction and a poroelastic medium. Using Timoshenko beam theory and Hamilton’s principle, electromechanical coupling equations are derived to govern the flexural vibration. Spectral element technology is applied to analyze the band structure, band gap (BG) distribution, and frequency response. Parametric studies validate the excellent vibration control effect and highlight the significant impacts of material, piezoelectric layers, feedback control, and flowing fluid on BG characteristics. This research provides a technological reference for vibration and elastic wave control in engineering composite pipe structures.