Mathematical models for two kinds of capacitor voltage transformer (CVT) with various states, i.e., zero load state, normal load state, short-circuit state of the primary side, and short-circuit state of the secondary side are presented. Digital simulation models of the CVT corresponding to the various states by using an adequate digital integration method are developed. Using the basis of these models, a digital simulation of the CVT on a PC is conveniently realized and transient characteristics of the CVT are researched on a PC according to the national lab standard, GB4703, of PR China. Details are demonstrated with the aid of a numerical example. The results indicate that the mathematical models and the digital simulation models are in good agreement.