Gearbox faults are the most important reason for failure of mechanical systems. In this paper, we propose a novel method for gearbox fault diagnosis based on vibration signal reported by accelerometers. We propose parametric power spectral analysis and support vector machine for feature extraction and classification, respectively. The proposed feature extraction technique reduces the dimensionality of the vibration signal and captures frequency characteristics simultaneously. We apply our technique to a well-known bearing benchmark dataset. The cross-validation indicates excellent performance and accuracy.