The current transformer conventionally employs a closed magnetic circuit design. But limited to the saturation of the magnetic core, when a short-circuit fault occurs in the primary coil, the DC current component will seriously affect the performance of the current transformer, leading to non neglectful errors ??for sensing the primary current. The air-gap-core current transformer increases the magnetic reluctance through the introduction of an air gap in the magnetic circuit, which can effectively reduce the core saturation with DC excitation. Based on fundamental equations of the magnetic and electrical circuits, an analytical model for the air-gap-core current transformer is presented with considering the loading effect of the secondary coil. Influences of different parameters on the air-gap-core current transformer are discussed. The established model supplies basic theoretical guidance towards compatibility of an air-gap-core current transformer for realizing both measurement and protection as well as improving the accuracy of a clamp current transformer that is used for power meter online calibration.