In this paper, a multiband stable domain method for designing and optimizing the machine/grid-side multi-channel supplementary damping controllers (MSDC) is proposed. On this basis, considering the maximized multi-band stability domain composed of TCSC conduction angles as the optimization objective and an optimization model is established. Furthermore, genetic algorithm is used to solve optimization model to obtain controller parameters that can maximize damping of system. Eigenvalue calculation and time-domain simulation show that the coordinative optimized damping controller can effectively suppress multi-band oscillations including low-frequency oscillation and subsynchronous oscillation.