Abstract: In view of the self-excited induction generator（SEIG） isolated system, the complex Hurwitz stability criteria was used to analyze its voltage build-up performance with and without loads. The state equations of SEIG were established based on the transient equivalent circuits under a static reference frame. The sufficient and necessary conditions for the stability of the SEIG, which was taken as an autonomous system, were given by complex Hurwitz stability criteria. And the critical parameters of voltage build-up of SEIG with and without loads were calculated. The results were verified to be correct compared with the experimental ones. Based on the self-excited voltage build-up process of SEIG, it is proved to be feasible to apply the complex coefficient Hurwitz criteria to the transient and steady stability analysis of SEIG. The conclusions of this paper lay a foundation for further applications of the complex Hurwitz criteria in SEIG stability analysis.