Voltage fault diagnosis and prognostics of lithium-ion batteries (LIBs) are critical in ensuring their safe and reliable operation, and timely voltage prediction can help detect the oncoming fault of LIBs effectively. To this end, this study develops an efficient voltage fault diagnosis and prognostic method for LIBs based on voltage prediction and multiple thresholds. Firstly, a hybrid neural network integrating convolutional neural network and gated recurrent unit is established to extract both temporal and spatial features from the current operation data and predict voltage. Then, a residual calculator is devised to generate the voltage residuals, and the maximum voltage residuals of the fault-free data during charge and discharge operations are leveraged to constitute the multiple thresholds of fault diagnosis and prognostics strategy. The robustness, reliability and feasibility of voltage prediction are validated under the conditions of different driving scenarios, different dynamic temperature and real-world operation data. Moreover, the validation results on the fault electric scooter reveals that the proposed method can reliably diagnose the battery over-voltage and under-voltage faults and their alarm levels. Additionally, the warning moment by this method is at least 630s earlier than the alarm time in the battery management system, highlighting its efficient prognostic functionality.