In this article, a robust output-feedback adaptive dynamic surface control (DSC) is proposed for linear time-invariant single-input single-output plants with unmodelled dynamics and unmeasurable output disturbance. With the proposed adaptive DSC scheme, the 'explosion of terms' problem inherent in backstepping control is eliminated and the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. More importantly, it is proved that with an initialisation technique, the L-infinity performance of the tracking error can be guaranteed even with unmodelled dynamics, bounded output disturbance exists and the plant high-frequency gain is unknown.