Abstract: Pipe conveying fluid is a typical fluid-structure interaction system in engineering. As the flow velocity increases, the interaction between fluid inertial forces, viscous forces, and the pipe's structural elastic forces can induce complex dynamic behaviors, leading to structural instability and significant nonlinear vibrations. Controlling such vibrations is crucial to ensure the safe operation of pipeline systems. Active control, which relies on system modeling, is an effective approach for suppressing structural nonlinear vibrations. However, developing low-dimensional mechanics model for pipe conveying fluid faces challenges such as high-dimensional strong nonlinearity and complex boundary conditions. To address these challenges, we propose a data-driven method based on spectral submanifolds for the modeling and vibration control of such systems. It takes the dynamic response of the pipe conveying fluid as observables and employs spectral submanifolds to learn the autonomous model of the system. The autonomous model is then refined using dynamic mode decomposition with control or long short-term memory neural networks to construct a reduced-order model with control. Finally, a linear-quadratic regulator or model predictive control is applied to compute optimal control inputs for vibration suppression. The effectiveness of the proposed method is demonstrated by suppressing nonlinear vibrations in pipes under various boundary conditions and flow velocities. Successful applications include the mitigation of buckling and flutter instability, as well as the control of chaotic motion.