The timely and effective fault diagnosis method is critical to the operation of the air-conditioning system and energy saving of buildings. In this study, a novel fault diagnosis method was proposed. It is combined with the signal demodulation method and machine learning method. The fault signals are demodulated by the demodulation method based on time-frequency analysis and principal component analysis (DPCA). The modulation characteristics of the principal component and DPCA sets with stronger features are obtained. Compared with time domain sets, the correct rate was increased by 16.38%. Then, as a machine learning method, the Visual Geometry Group—Principal Component Analysis (VGG-PCA) model is proposed in this study. The application potential of this model is discussed by using evaluation indexes of fault diagnosis performance and two typical faults of air conditioning systems. Compared with the other two convolution neural network models, the correct rate was increased by 17.1% and 20.32%, and the running time was reduced by 69.25% and 64.53%, respectively. A large number of tests are used to investigate the optimal range of model parameters. This provides the reference and guarantee for further model optimization.