This paper proposes a unified power-flow controller (UPFC) to suppress subsynchronous resonance (SSR) occurred in a hybrid power-generation system connected to an infinite bus through a series-capacitor compensated line. The hybrid power-generation system contains a steam-turbine generator (STG) and an offshore wind farm (OWF) based on doubly-fed induction generator (DFIG). The d-q axis equivalent-circuit model under three-phase balanced loading conditions is derived to establish the complete system model including the STG set, the DFIG-based OWF, the series-capacitor compensated line, the UPFC, etc. A damping controller of the proposed UPFC is designed by using pole-assignment approach based on modal control theory to effectively damp out unstable STG modes of the studied system. Both small-signal stability and transient simulation results of the studied system are systematically performed. The simulation results show that the proposed UPFC joined with the designed damping controller can effectively suppress unstable STG modes of the studied power system.