The parametric fuzzy sliding mode control (FSMC) and parametric fuzzy neural network control (FNNC) methods, in the present study, is applied to suppress vibration of the axially moving string system, which is driven by adjusting the axial tension. Due to the difficulty of utilizing fuzzy logic control (FLC) to obtain the linguistic control rules, the stability and robustness are not guaranteed. The sliding-mode control is then incorporated in the scheme of FLC to generate the control rule bases in order to meet the requirement of stability and robustness. In additions, for the purpose of improving system performance, the Genetic Algorithm (GA) is applied to search for the optimal parameters of the fuzzy sliding mode controller. Beside the aforementioned method of fuzzy sliding mode control plus GA, the on-line learning algorithm Fuzzy Neural Network (FNN) accompanied with sliding mode characterization is also developed and applied to achieve control goal. In this method, the parameters of FNN are adjusted in the direction that minimizes sliding mode variables SṠ where S of the switching function for vibration suppression. Simulations are conducted to verify the effectiveness of control designs. The results show the performance of FSMC with GA in general is favorable to others.