The equivalent inertia of power system is reducing with the increasing wind power penetration. To alleviate this issue, more and more countries have put forward grid codes which require wind farms (WFs) to perform inertia control so as to provide synthetic inertia response as traditional synchronous generation (SG) does. It is found in this paper that the inertia control of the WF in a weak grid deteriorates drive-train torsion of wind turbine generators (WTGs). Furthermore, the WF emulating inertia response is involved in power system oscillations and a new critical low frequency oscillation mode is induced by the WF. These two potential risks restrict the WF to fulfill grid code requirements. To overcome this problem, this paper proposes a two-level damping control scheme consisting of a WTG level torsional oscillation damping control and a WF level low frequency oscillation damping control to enhance damping characteristic of the WF. Simulation results show that the two-level damping control can counteract these potential risks and facilitates the WF to meet grid code requirements.