Abstract: Studies in recent years have shown that in addition to the ability to provide frequency and voltage support for AC system, the voltage-controlled virtual synchronous generators（VSG） are also of good adaptability to the operation conditions of weak grid. To improve the stability of a grid-connected VSG and exploit its advantages to the full, in this paper, a method to determine the critical short-circuit ratio（SCR） of the gird-connected VSG system and related stability criteria are explored considering small-signal stability（SSS）. To do so, the small-signal model of a grid-connected VSG system is established and sorted into a form of negative feedback system with two-input and two-output units at first. Secondly, according to the generalized Nyquist criterion, a SSS criterion for the system considering impact of grid strength is proposed and a critical SCR is defined, which can provide guidance and reference for planning of gird-connected VSG systems in the future. Finally, methods proposed in the paper are validated through study cases.