A superconducting magnet system is developed for the application of high frequency gyrotrons at XXX. The operation cost for the magnet is dominated by refrigeration power. To reduce the heat load for cryogenic system, a pair of YBCO binary current leads is designed in consideration of the industrial concentration on type II high temperature superconducting (HTS) YBCO material. In this paper, a simulation model is proposed to perform the electromagnetic-thermal coupling analysis of these YBCO binary leads under different operation conditions by combining Partial Element Equivalent Circuit (PEEC) method and Finite Volume Method (FVM). The simulation code can improve computational efficiency and enable high-accuracy coupling between the electromagnetic field and heat transfer process. Under steady state, the heat leakage at 4.2 K cold end of YBCO binary leads depends mainly on the geometric parameters of YBCO tape, especially the cross-sectional area of the copper layer in YBCO tape. The cooling mode and liquid helium level also have a significant impact on the heat leakage level. The optimal outer diameter of the normal copper section is identified, and the optimum value is largely influenced by the effective cooling power imposed on the cold end of the normal copper section. Under transient state, the simulation for charging process and the loss of cooling accident are performed, along with the detailed analysis of the electromagnetic-thermal response features of the leads under these conditions. The results indicate that the YBCO binary current leads possess high thermal stability and an ample time margin for the magnet system to be demagnetized.