Abstract: The virtual synchronous generator (VSG) may have problems that the system bifurcation curve changes and the VSG voltage drops or rises due to catastrophe phenomena during operation, which is not conducive to the stable operation of the VSG. To address these problems, a VSG mathematical model with direct current bus capacitor voltage equation as the swing equation was firstly established. Secondly, the catastrophe phenomenon occurring in the VSG under the variations of internal parameters and external operating conditions were respectively discussed and the catastrophe mechanism was revealed based on the bifurcation and catastrophe theories. Then, the parameter stability regions were partitioned and the correctness of the partitioned regions were verified by time-domain simulation. Finally, the effect of catastrophe on VSG's voltage support capacity was analyzed. The results show that the catastrophe occurs through saddle-node bifurcation points and changes with different parameters; the VSG voltage support capability increases when catastrophe occurs with voltage dropping, while the VSG voltage support capability decreases when catastrophe occurs with voltage swelling; within the parameter stability regions, the VSG is not subject to catastrophe.