Flexible-link robot arms have advantages over the conventional ones such as less weight, less energy consumption, and smaller actuators. However, a disadvantage of the manipulators is the vibration occurred inherently due to the flexible behavior of the arms during operation. This situation may effect control performance in some applications, for example, the use of the robot for fine painting or welding. This paper describes vibration suppression of a two-link flexible manipulator by means of fuzzy sliding mode control based neural network-like structure. Simulation and experimental results shows an effectiveness and control performance of the proposed method for vibration suppression of the robot links.