The interactions between grids and power converters can easily lead to performance degradation or even instability, especially in weak grids where grid impedance can change frequently and significantly. A loop gain based auto-tuner is proposed in this work for power converters to maintain high control performance and robust grid-converter connection. The auto-tuner is designed to autonomously adjust controller's parameters (e.g., proportional gain and integral gain) of power converters based on real-time estimated loop gain. Compared with impedance reshaping methods, the proposed solution requires no additional hardware and guarantees simultaneously high control performance and sufficient stability margins. Experimental results are given for validating the effectiveness of the proposed method.