The problems of strong linear indistinguishability of different fault features and insufficient labeling of fault data exist in bearing compound fault classification, which seriously affect the classification accuracy. This paper proposes a semi-supervised compound fault classification method based on the two-stage SVM with wavelet kernel diffusion. To address the strong linear inseparability of fault features, the wavelet kernel function is used to transform them in high-dimensional space, and the maximal overlap discrete wavelet packet transform is applied to obtain the energy distribution of the signal in different frequency bands as the fault features. Aiming at the insufficiency of the fault data labeling, a two-stage SVM classification model with incremental kernel space label diffusion is proposed. Based on the kernel difference distance in the wavelet kernel space, we expand the neighboring samples and boundary samples in the coarse partition stage using incremental kernel space label diffusion, and the training of models is completed based on expanded samples at the segmentation phase. Three sets of bearing composite fault data validate the effectiveness of the proposed method, and the experimental study shows that under the condition of a single class of training samples of 5, the proposed method improves the classification accuracy by 7. 5% on average than SVM, and outperforms other popular algorithms.