Multimodal sub-synchronous resonance (SSR) induced by the interactions between the generator shafts and the fixed series capacitors has become a serious threat for the power system. To overcome this, a voltage source converter (VSC) based controller for multimodal SSR suppression, named sub-synchronous resonance dynamic suppressor (SSRDS), is presented and analyzed in this paper. The controller is placed at the point of common coupling (PCC) of the power plant for multi-generator SSR suppression purpose so that the investment costs can be minimized while making sure the requirements of the SSR damping. To quantify the contribution of SSRDS to the SSR damping, the damping torque analysis is carried out, which can reveal the influences of the operating conditions and the correlated control parameters on the damping performance. Furthermore, to avoid the negative affects between the different TMs in close range as well as maximize the damping ability of SSRDS, the parameters tuning method of the mode filters and the gain and phase shifters are proposed. A detailed nonlinear simulation model is established in PSCAD/EMTDC based on the Jinjie series compensated transmission system located in China. The damping torque analysis, the eigenvalues analysis and the simulation results have fully demonstrated the effectiveness and the robustness of the proposed SSRDS for multi-generator and multimodal SSR suppression under both small and large disturbances in various operating conditions.