The rapid and accurate diagnosis of power grid faults plays a vital role in speeding up the process of accident handling and system recovery and ensuring the safe operation of the power system. This paper proposes to apply the ensemble empirical mode decomposition (EEMD) method and scale-related intrinsic entropy to diagnose the type of fault for the transmission line. First, the electrical data collected by the power system is decomposed by using the EEMD method. Then by eliminating some intrinsic mode functions, the signal is reconstructed by inspecting the correlation coefficient. Finally, the complexity of the reconstructed signal is calculated by using the scale-dependent intrinsic entropy. Since the scale-dependent intrinsic entropy reflects the complexity of one-dimensional time series, it is susceptible to signal changes. The complexity is helpful in the power system for fault signal analysis. The results show the combined method’s effectiveness and practicability through failure analysis using the IEEE 14-bus system as the simulation model.