This paper proposes a nonlinear electromagnetic-thermal-velocity coupling model to study the insulation performance of converter transformer, in which the saddle-like electric-stress dependence is considered under compound alternating current-direct current (AC-DC) voltage situation. Firstly, the conductance of transformer oil and oil-immersed pressboard have been measured through constructed threeelectrode experimental system. An interesting electric-stress characteristic, which is saddle-like electricstress dependence is obtained and counted in the thermal-insulation analysis in the proposed model. Then, the high-order harmonics of compound AC-DC voltage have been considered in the built electromagneticthermal-velocity coupling model. Additionally, the impact of non-uniform temperature result has been mapped to the electric field domain through interpolation method, due to different meshes between the flowthermal and electric fields in accordance with distinct computational characteristics. Finally, the performance of nonlinear thermal-electric coupling properties, including saddle-like electric-stress dependence, have been considered in the proposed coupling model. Results determine that saddle-like thermal-electric dependent properties would considerably change insulation capability, compared with results from the traditional method. Even intensity field of some sampling points could jump more than 1.6 kV/mm. Therefore, it is essential to evaluate the insulation design by practical saddle-like electric-dependent properties. INDEX TERMS Compound ac-dc voltage, converter transformer, electric-stress dependence, finite element sub-model, electromagnetic-thermal-velocity coupling.