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For a single-machine infinite-bus system with thyristor controlled series capacitor(TCSC), a new approach is proposed to solve Hopf bifurcation point of dynamic voltage stability by reduced order, and the feature of the proposed approach is to reduce the order of a (3n+2)-dimensional Newton iterative equations to a (n+2)-dimensional linear equations. Comparing with traditional direct calculation method, the calculation burden can be mitigated and avoided curse of dimensionality, so it is suitable to the analysis and calculation of dynamic voltage stability of a single-machine infinite-bus system. By the nonlinear analysis software package-Auto97, the dynamic voltage stability of a single-machine infinite-bus system is studied in detail with the method proposed in this paper. The test in this example shows that the bifurcation theory can be more accurate than the linearization method in analyzing the dynamical stability near the critical point of the power systems.