In this paper, a vibration signal-based hybrid diagnostic method, including vibration signal adaptive decomposition, vibration signal reconstruction, fault feature extraction, and gearbox fault classification, is proposed to realize fault diagnosis of general gearboxes. The main contribution of the proposed method is the combining of signal processing, machine learning, and optimization techniques to effectively eliminate noise contained in vibration signals and to achieve high diagnostic accuracy. Firstly, in the study of vibration signal preprocessing and fault feature extraction, to reduce the impact of noise and mode mixing problems on the accuracy of fault classification, Variational Mode Decomposition (VMD) was adopted to realize adaptive signal decomposition and Wolf Grey Optimizer (GWO) was applied to optimize parameters of VMD. The correlation coefficient was subsequently used to select highly correlated Intrinsic Mode Functions (IMFs) to reconstruct the vibration signals. With these re-constructed signals, fault features were extracted by calculating their time domain parameters, energies, and permutation entropies. Secondly, in the study of fault classification, Kernel Extreme Learning Machine (KELM) was adopted and Differential Evolutionary (DE) was applied to search its regularization coefficient and kernel parameter to further improve classification accuracy. Finally, gearbox vibration signals in healthy and faulty conditions were obtained and contrast experiences were conducted to validate the effectiveness of the proposed hybrid fault diagnosis method.