AbstractConventional synchronous generators have been replaced by renewable energy source such as photovoltaics generation and wind turbine generation interconnected through inverters. As the capacity of synchronous generators interconnected to the power system decrease, the power system stability can be gradually jeopardized. Therefore, these inverters may be required to have some control functions in grid‐interconnection code to support power system stabilization. On the other hand, it is known that the response of some control functions become unstable and undesired oscillatory behavior appears depending on the power system conditions such as low short circuit ratio. In consequence, not only the expected power system stabilization is not obtained, but also the power quality may be degraded. In this paper, the mechanism of these instabilities is clarified by using a simplified root mean square model, and a damping controller applicable to grid‐following (GFL) inverter is developed. It is shown that the damping of the oscillatory behavior could be improved by applying the proposed controller using eigenvalue analysis and time domain simulation. This contribution is useful for the appropriate operation of the control function installed to GFL inverter.