To improve the transient stability of an AC/DC hybrid grid, this paper designs a Nonlinear Adaptive Wide-Area Supplementary Controller (NAWSC) based on the large signal modulation of High Voltage Direct Current (HVDC). Without an accurate model, the proposed controller can directly estimate and compensate for the nonlinear dynamics in the actual system using a disturbance observer. It can also tackle the problem that it is difficult to design corresponding control measures when the model is uncertain. Equivalent wide-area power angle information is used for output feedback to realize transient stability control directly. Two case studies are undertaken based on a four-machine two-area AC/DC hybrid grid and a 10-machine 39-bus AC/DC hybrid system. The simulation results show that compared with a proportional integration wide-area supplementary controller, NAWSC possesses better adaptability under different operating conditions. When the uncertainty of parameters is taken into account, NAWSC possesses better control robustness compared with a feedback linearized wide-area supplementary controller. Based on the accurate model, NAWSC can improve the transient regulation capability of HVDC. This work is supported by the Science and Technology Project of State Grid Corporation of China “Technical Research of Grid-Source Coordination Performance Assessment and Optimization based on Generator Performance Differentiation and Power Grid Dominated Stability” (No. SGZJ0000KXJS1800293 and No. 521104180019).