Due to impedance interaction, the sub-synchronous resonance (SSR) issue of the renewable energy generation (REG) system connected to weak grid has recently become prominent. Firstly, the mechanism and characteristics of the SSR occurring in the REG system under weak grid are analyzed based on the impedance method. With the decline of grid stiffness, the REG system can easily cause SSR owing to the impedance interaction between the inductive grid impedance and the capacitive REG system impedance in the low frequency range. To suppress this SSR, an inertia phase locked loop (IPLL) is proposed, which can optimize the impedance of the REG system in the low frequency range. According to the impedance based SSR analysis, the REG system with the proposed IPLL can hardly cause SSR under weak grid. Moreover, the mechanism, characteristics and design method of the proposed IPLL is introduced in detail. By using the proposed IPLL, the SSR issue of the REG system under weak grid can be effectively solved. Finally, the theoretical analysis and the proposed mitigation method of SSR are validated with the simulation and experimental study.