This study presents a fractional-order adaptive high-gain controller for control of depth of anaesthesia. To determine the depth of anaesthesia, the bispectral index (BIS) is utilised. To attain the desired BIS, the propofol infusion rate (as the control signal) should be appropriately adjusted. The effect of the propofol on the human body is modelled with the pharmacokinetic–pharmacodynamic (PK/PD) model. Physical properties of the patient such as gender, age, height and a like determine the parameters of the PK/PD model. This necessitates us to employ an appropriate adaptive controller. To attain this goal, a fractional-order adaptive high-gain controller is constructed to solve the tracking problem for minimum phase systems with relative degree two (such as the PK/PD model). This leads to a time-varying gain adjusting according to a fractional-order adaptation mechanism. Simulation results performed on various patients (considering the external disturbance and the measurement noise) show the effectiveness of the proposed method.