This paper presents a procedure for designing a supplementary damping stabilizer for a static synchronous series compensator(SSSC) in multi-machine power systems.The objective is to shift the lightly damped inter-area modes toward the prescribed stability region.A lead-lag stabilizer is used to demonstrate this technique,in which a particular measure of stabilizer gain is considered as an objective function.Constraints of the problem for phase-lead and lag structures are derived.The objective function with the constraints is formed as a quadratic mathematical programming problem.For robust design,the parameters of the stabilizer are calculated under various operating conditions.Two types of SSSC-based stabilizer have been presented and designed.Numerical results including eigenvalue analysis and the nonlinear simulations on the 4-and 50-machine power systems are pre-sented to show the effectiveness of the proposed method. This paper presents a procedure for designing a supplementary damping stabilizer (SSSC) in multi-machine power systems. The objective is to shift the lightly damped inter-area modes toward the prescribed stability region. A lead-lag stabilizer is used to demonstrate this technique, in which a particular measure of stabilizer gain is considered as an objective function. Constraints of the problem for phase-lead and lag structures are derived. The objective function with the constraints is formed as a quadratic mathematical programming problem For robust design, the parameters of the stabilizer are calculated under various operating conditions. Two types of SSSC-based stabilizers have been presented and designed. Numerical results include eigenvalue analysis and the nonlinear simulations on the 4-and 50-machine power systems are pre-sented to show the effectiveness of the proposed method.