The probability of multi-faults in a power grid can increase because of both the internal and external environment. A key transmission section identified by analysis of typical power system operating modes may not reflect the weakness of the power grid after faults when the grid structure is seriously damaged. Therefore, a key transmission section identification method considering multi-faults is proposed. First, according to variation of branch load rate and consistency discrimination of flow direction, power flow transfer channels of faults are identified. Secondly, based on power flow transfer characteristics of different faults, an incidence matrix of fault elements and power flow transfer channels is constructed by line tripping distribution factors. Candidate key transmission sections consist of fault channels and power flow transfer channels which are strongly relevant. Lastly, the thermal stability margin of each candidate section is calculated by a linear programming method. Sections whose margin is lower than the thermal stability margin threshold are selected as key transmission sections of thermal stability. The effectiveness of the proposed method is verified by a practical power grid example. This work is supported by the National Key Research and Development Program of China (No. 2018YFB0904500) and the Science and Technology Project of State Grid Jiangsu Electric Power Co., Ltd. (No. SGJS0000DKJS1900558).