In this paper, we propose an improved sub-synchronous resonance (SSR) damping controller (SSRDC) and a related control strategy to mitigate the SSR in a capacitive series-compensated double-fed induction generator based wind farms, based on the damping torque analysis. The proposed strategy is utilized for enhancing the system stability. Compared with the traditional damping controller, the proposed SSRDC is simultaneously embedded into the d-axis and q-axis control channels in the inner current loop of the rotor-side converter. On this basis, combined with the eigenvalue analysis and improved particle swarm optimization algorithm, the optimum gain coefficients of the SSRDC can be determined for maximizing the mitigation effect under different operation conditions of the series compensation levels and wind speeds. Moreover, the effect of the weight coefficients in the objective function on the SSR suppression is also investigated. Finally, the time-domain simulations are carried out to demonstrate the effectiveness of the proposed control strategy for mitigating the SSR and suppressing the connected power system oscillations.