A pattern classification method based on α-stable distribution and support vector machine (SVM) is proposed, aiming at the extraction of the pulse characteristics of vibration signals from rolling bearings with faults. First, the α-stable distribution is defined, and its probability distribution function (PDF) is introduced and compared with the PDF of the vibration signals from the faulted bearing. The comparison results confirm that the vibration signals with pulse characteristics agree with the α-stable distribution. Then, the measured signals from different bearings are decomposed by wavelet packet decomposition, and the relevant characteristics parameters are computed and selected as eigenvectors that can be used to classify feature patterns based on SVM. Comparing the presented method with the traditional method illustrates its better classification performance.