Abstract: The concept of complex torque coefficient was extended to the design of HVDC supplementary controller. By scanning the AC/DC system in low frequency band, the frequency domain characteristics of controller were derived, which should satisfy the desired performance and stabilize the system. Setting the frequency domain characteristics as constraint conditions, the structure and the parameters of the controller can be determined. The index curves obtained are visible and intuitional, easy to analyze the effects of system parameter variations on the controller performance, and helpful to gain the robust controller. In the twoarea fourmachine system of the case study, the results show that under various operation conditions, the supplementary controller can damp out the low frequency oscillations.