Gallium nitride(GaN) devices have great potential in high-frequency and high power density converters. And GaN devices are more and more used into synchronous rectifier circuits. However, the high switching speed of GaN device makes it prone to have switching oscillation problems. Considering the low loop damping determined by the low on-resistance characteristic of the device and compact PCB design, the oscillations can even be sustained, affecting the circuit stability. In order to solve this problem, RC damper is paralleled to the drain-source of the synchronous rectifier device. The suppression mechanism is explained from the aspect of loop conductance matching based on oscillator theory. And a modified negative conductance model of the GaN-based synchronous rectifier circuit is established. Based on the established model, the optimized design method of the RC parameters is proposed. The method is verified to be effective by experiments. In addition, power loss analysis of the RC damper has also been analyzed.