Abstract: Pipes conveying fluid are widely used in important engineering fields such as machinery, aviation, nuclear power and petroleum industries. In order to prevent the damage of pipeline structures due to flow-induced vibrations, it is necessary to conduct in-depth research on the stability, dynamic response and regulation of pipes conveying fluid. This paper proposes a grounded absorber model composed of an inerter, a spring and a damper in parallel, and studies the influence of this grounded absorber on the stability and nonlinear vibrations of the cantilevered pipe conveying pipe. First, a nonlinear dynamical model of the non-conservative system with a grounded inerter-based absorber is introduced based on Hamilton's principle. Then, the nonlinear governing equation is discretized using a high-order Galerkin method. Finally, the passive control effect of the cantilevered pipe under different absorber parameters is analyzed from both linear and non-linear perspectives, and the influence mechanism of the inertia coefficient and the installation position of the vibration absorber on the stability and dynamic responses of the cantilevered pipe are discussed. The results based on the linear theoretical model show that the grounded inerter-based absorber can significantly affect the critical flow velocity of the cantilevered pipe, and hence the stability of the pipe can be effectively improved by adjusting the parameters of the vibration absorber. The control effect of the inertia coefficient and spring stiffness on the stability of the system is found to be closely related to the installation position of the vibration absorber. The results based on the nonlinear theoretical model show that the nonlinear dynamic responses of the pipe conveying fluid are also significantly affected by the inertia coefficient and the position of the vibration absorber, and this effect depends on the value of the flow velocity of the pipe. Under certain parameter conditions, the vibration absorber can evolve the pipe conveying fluid from periodic motion to complex chaotic behavior. The results obtained in this paper demonstrate that by designing reasonable parameters of the inerter-based absorber, the stability of the cantilevered pipe conveying pipe can be improved and the vibration amplitudes of the pipe can be effectively suppressed.