When a rolling bearing fails, it is usually difficult to determine the degree of damage. In light of this problem, a new fault diagnosis method is presented to achieve feature extraction and intelligent classification of different fault positions and degrees of damage of rolling bearing signals. First, the alpha -stable distribution of four parameters of the vibration signals of each status is estimated. Next, the two parameters that are the most sensitive and stable are found and employed as fault feature values. Feature values are regarded as the input of least squares support vectors machine (LSSVM) based on particle swarm optimization (PSO) for judging the fault position and degree of damage of the rolling bearing. Finally, the method′s effectiveness is verified by bench test data, and the method is compared with other related methods. The results show that the presented method can accurately achieve the intelligent diagnosis of the fault positions and degree of damage of rolling bearings, has better generalization than LSSVM or support vectors machine (SVM) methods that are not optimized by PSO, and has the potential to solve practical engineering problems.