Abstract: Due to the negative resistance characteristic of power electronic device, the small-signal stability in a multiple grid-connected-converter system (MGCCS) is facing many challenges. The impedance analysis method and state space analysis method in the analysis of a MGCCS has some limitations. In this paper, a stability analysis method for MGCCS based on a sufficient stability criterion was proposed. Firstly, MGCCS was modeled as a medium and high dimensional negative feedback system with a stable open-loop function. Secondly, a sufficient stability criterion with low complexity was developed through estimating the eigenvalue of the open-loop function. And a corresponding parameter sensitivity analysis was proposed by using the developed criterion. Finally, a 7-infeed converter system with stability problem was used to verify the effectiveness of the proposed method. Theoretical analysis and nonlinear simulation showed that the criterion in this paper could accurately judge the stability of the system with low complexity. In addition, the parameter sensitivity analysis could provide a guidance for the parameter optimization of the system.