Pumped storage units serve as a crucial support for power systems to adapt to large-scale and high-proportion renewable energy sources by providing a stable and flexible energy supply. However, due to the coupling effects of electric power load demands and the complex multi-source factors within the water–mechanical–electrical system, the interrelationship between unit parameters becomes more intricate, posing significant threats to the operational reliability and health status of the units. The complexity of fault diagnosis is further aggravated by the intricate and varied nature of fault characteristics, as well as the challenges in signal extraction under conditions of strong electromagnetic interference and high noise levels. To address these issues, this paper proposes a novel data-model hybrid-driven strategy that analyzes vibration signals to achieve rapid and accurate fault diagnosis of the units. Firstly, the spectral kurtosis theory is employed to enhance the traditional empirical mode decomposition, achieving optimal decomposition and noise reduction effects for vibration signals. Secondly, the intrinsic mode functions (IMFs) obtained from the decomposition are reconstructed, and the entropy values of effective IMFs are calculated as fault feature vectors. Subsequently, the CNN-LSTM model is utilized for fault diagnosis. The effectiveness and feasibility of the proposed method are verified through actual operational data from pumped storage units in a specific region. Through analysis, the fault diagnosis accuracy of the method proposed in this paper can be maintained above 95%, demonstrating robustness in complex engineering environments and effectively ensuring the safe and stable operation of pumped storage units.