In this paper, a static synchronous series compensator (SSSC) combined with a fixed capacitor, which is called hybrid series compensation (HSC), is proposed to avoid subsynchronous oscillation (SSO) in a series compensated transmission system and its characteristic is studied based on IEEE first benchmark model for SSO analysis. By employing the complex torque coefficient method and time-domain simulation, the performance of HSC on damping SSO is analyzed in the aspects of component proportion of HSC, installation location and control strategy mode. A supplementary sub-synchronous damping controller (SSDC) for SSSC is also designed to increase the damping performance of HSC at critical oscillation frequency.