We present a state-feedback control of a two-link flexible-joint robot. First, we obtain desired control laws from Lyapunov's second method. Then, we use three-layer neural networks to learn unknown parts of the desired control laws. In this way, the control algorithm does not require the mathematical model representing the robot. We use smooth variable structure controller to handle the uncertainties from neural network approximation and external disturbances. To show the effectiveness and practicality of this control algorithm, we performed an experiment on one of the robots in our laboratory.