This study is dedicated to design effective control schemes to suppress transverse vibration of an axially moving string system by adjusting the axial tension of the string. To this end, a continuous model in the form of partial differential equations is first established to describe the system dynamics. Using an energy-like system functional as a Lyapunov function, a sliding-mode controller (SMC) is designed to be applied when the level of vibration is not small. Due to non-analyticity of the SMC control effort generated as vibration level becoming small, two intelligent control schemes are proposed to complete the task -fuzzy sliding-mode control (FSMC) and fuzzy neural network control (FNNC). Both control approaches are based on a common structure of fuzzy control, taking switching function and its derivative as inputs and tension variation as output to reduce the transverse vibration of the string. In the framework of FSMC, genetic algorithm (GA) is utilized to search for the optimal scalings for the inputs; in addition, the technique of regionwise linear fuzzy logic control (RLFLC) is employed to simplify the computation procedure of the fuzzy reasoning. On the other hand, FNNC is proposed for conducting on-line tuning of control parameters to overcome model uncertainty. Numerical simulations are conducted to verify the effectiveness of controllers. Satisfactory stability and vibration suppression are attained for all controllers with the findings that the FSMC assisted by GA holds the advantage of fast convergence with a precise model while the FNNC is robust to model uncertainty and environmental disturbance although a relatively slower convergence could be present.