The vibration signals coming from a hydropower unit have strong nonstationary characteristics when strong vortex develops in the hydraulic turbine draft tube. Related to this problem, a new vibration analysis method for a hydropower unit based on adaptive local iterative filtering is proposed. Firstly, adaptive local iterative filtering was used to decompose the complex vibration signal into several intrinsic mode functions. Then, frequency spectrum analysis of these components was performed to obtain the vortex characteristic frequency from the vibration signal. Simulated and real-world signals were used to verify the proposed method. The obtained results show that this method can overcome the problem of mode mixing in the existing empirical mode decomposition method, since it improves the efficiency and accuracy of feature extraction for nonstationary vibration signals from a hydropower unit.