Compared with the laminated core transformer (LCT), the 3D wound core transformer(3D-WCT) has the characteristics of symmetrical magnetic circuit and low vibration. This article focuses on the modeling and optimal design of the 3D-WCT for isolated DC/AC application. Firstly, based on the Jiles-Aterton model, a nonlinear magnetic circuit model of the 3D-WCT is established to calculate the flux density and core loss accurately under SPWM excitation. A thermal network model is presented for the steady-state temperature-rise calculation of the forced-air cooled 3D-WCT. Secondly, the optimal design method is carried out on the basis of the magnetic circuit and thermal network models. Based on the optimized design results, a regression analysis is performed to establish the relationship between the design variables and the performance objectives. Finally, a 75kVA 3D-WCT prototype is manufactured and tested in the actual inverter power supply to verify the established magnetic circuit and thermal network models. The 3D-WCT prototype is applied to the 150kVA inverter power supply, which contributes to achieving high power density and high efficiency of the power supply.