The invention relates to the field of power transmission and distribution of an electric power system and harmonic wave suppression, especially to a mathematic model of a four-winding induction filtering transformer and an equivalent circuit thereof. According to correlation theories of a multi-winding transformer and a zero-equivalent impedance characteristic of an additional filtering winding of a four-winding induction filtering transformer, a simplified mathematic model and the four-winding induction filtering transformer and a ray equivalent circuit thereof are deduced; and all obtained impedance parameters of the ray equivalent circuit are equivalent impedance value or short-circuit impedance values of all windings of the four-winding induction filtering transformer. All parameters in the circuit are simple, clear, and are easy to calculate. An effective method is provided for analyzing operating characteristics of the four-winding induction filtering transformer.