An intelligent diagnosis method based on support vector machine (SVM) is proposed to quantitatively diagnose early weak faults of high-speed aero-engine’s bearings. In order to achieve a better performance in contrast with conventional kernel function, a mixed kernel function is constructed and particle swarm optimization (PSO) is used to optimize kernel coefficients and other parameters. Experimental raw data is preprocessed by sparse decomposition and reconstruction method to remove noise in original signals, which can provide effective and reliable samples for SVM. In order to verify the validity of the proposed method, experiments on different fault types with different defect sizes of high-speed bearings working at 30000rpm are carried out. The results show that the accuracy of the proposed method is greatly improved compared with traditional SVM. The proposed method can not only distinguish different types of failure but also distinguish different degrees of the same fault pattern, which achieves a quantitative intelligent diagnosis of early weak faults in aviation’s high-speed bearings.