Hybrid series compensation using static synchronous series compensator (SSSC) and passive series capacitor can improve the stability of the system, increases the power transfer capability and is useful for the fast control of power flow. This paper analyzes the subsynchronous resonance (SSR) characteristics of the hybrid series compensated power system in detail and proposes a simple method for the extraction of subsynchronous components of line current using filter. The extracted subsynchronous frequency component of line current is used to inject a proportional subsynchronous voltage in series with the transmission line which suppresses subsynchronous current in the transmission network. This novel technique is termed as subsynchronous current suppressor. The design of subsynchronous current suppressor is based on damping torque analysis and using genetic algorithm. A novel graphical representation of series resonance condition when SSSC is incorporated in the system is presented. The detailed study of SSR is carried out based on eigenvalue analysis, transient simulation and damping torque analysis. The results of the case study on a system adapted from IEEE First Benchmark Model demonstrates the effectiveness and robust performance of subsynchronous current suppressor in damping of SSR under various system operating conditions. Linear analysis is performed on D-Q model of the system with SSSC and the results are tested by executing transient simulation based on detailed nonlinear three-phase model.