Signals of a faulty building electrical system contain a large amount of information about the electrical systems operating status. However, it is difficult to extract the fault features completely because of their characteristics of non-linearity and non-stationarity which brings a problem of a relatively low fault identification rate of the current fault diagnosis methods based on pattern recognition. Aiming at improving the accuracy of fault diagnosis further, this paper proposes a fault diagnosis method of a building electrical system based on the complementary ensemble empirical mode decomposition and mutual dimensionless index extraction (CEEMD-MDI) combined with the multi-kernel relevance vector machine (MK-RVM). First, the resistance signals of a faulty building electrical system are decomposed into a series of intrinsic mode functions (IMFs) by using an adaptive decomposition ability of the CEEMD. Second, the IMFs are used to extract the mutual dimensionless index (MDI) and to form a feature vector with the resistance signal. Finally, the processed feature vector is input into the MK-RVM for modeling, and the fault diagnosis result of the building electrical system is provided in the form of a probability output. The experimental results show that the fault diagnosis accuracy rate of the proposed method based on CEEMD-MDI and MK-RVM can reach 97.22%, which has better fault diagnosis performance compared with other methods.