The purpose of this paper is to investigate the dynamic behavior of a fluid conveying pipe and to propose suitable control strategies in order to eliminate or suppress its vibration. The system under consideration consists of a uniform, straight, vertical cantilever pipe which conveys incompressible fluid. Governing equation of motion for free transverse vibration is derived by using Newtonian approach. This equation is discretized using the finite element method. The effects of the fluid flow speed on open loop response of the system are investigated. The results show unstable behavior when the flow velocity exceeds a critical value. Neural network based controller are applied to the system to suppress the pipe vibration and to improve the stability conditions. The results show that neural network based controller successfully suppresses the vibration when the critical flow velocity is exceeded. Moreover, it holds the system response in the stable region at higher flow velocities. NN based controller learns the variation of the system against unknown flow velocities in the system and adapts itself against unknown changes.