Bearing fault diagnosis has attracted significant attention over the past few decades. In this paper, Alpha-stable distribution was introduced for feature extraction from faulty bearing vibration signals. Such a non-Gaussian model can accurately describe statistical characteristic of bearing fault signals with impulsive behavior. After extracting feature vectors by Alpha-stable distribution parameters, the weighted support vector machine (wSVM) was applied to automate the fault diagnosis procedure. Simulation results demonstrated that the proposed method is a very powerful algorithm for bearing fault diagnosis and has much better performance.