In order to effectively extract the characteristics of nonstationary vibration signals from hydropower units under noise interference, an adaptive stochastic resonance and Fourier decomposition method (FDM) based on genetic algorithm (GA) are proposed in this paper. Firstly, GA is used to optimize the resonance parameters so that the signal can reach the optimal resonance and the signal-to-noise ratio (SNR) can be improved. Secondly, FDM is used to process the signal and the appropriate frequency band function is selected for reconstruction. Finally, Hilbert envelope demodulation analysis was performed on the reconstructed signal to obtain the fault characteristics from the envelope spectrum. In order to prove the effectiveness and superiority of the proposed method, comparative experiments are designed by using the simulated signal and the measured swing signal of a hydropower unit. The results show that this method can effectively remove the noise interference and improve the SNR and extract the characteristic frequency of the signal, which has the extensive engineering application value to the fault diagnosis of hydropower units.