Based on the characteristics of three-phase three-limb transformer magnetic circuit，the relationship among its inductances is analyzed，and a new mathematical model and an equivalent circuit model are proposed.The proposed model can reflect the structure characteristics of three-phase three-limb transformer magnetic circuit.Compared with existing three-phase three-limb transformer models，the new model can clearly demonstrate the roles of each current component in inducing winding voltage.The equivalent circuit model is more simple and intuitive than existing models and is easy for qualitative analysis and calculations.The proposed model is verified through comparison with the traditional nonlinear three-limb transformer model.As an example for application，the simplified calculation model for three-phase three-limb transformer with external faults is discussed.