Reliable prediction of the remaining useful life (RUL) of the battery is capable of providing a critical reference decision for users to use and replace batteries. Although there are many methods for battery RUL prediction, these methods suffer from insufficient training, ignoring local regeneration of capacity degradation curves, complex structure and a wide range of optimization seeking parameters, so this paper proposes a hybrid battery RUL prediction method. In the data processing stage, adaptive noise complete ensemble empirical modal decomposition (CEEMDAN) decomposes the battery capacity sequence, then calculates the fuzzy entropy value of each component and reconstructs the components with similar entropy values. In the model training stage, two data and model class methods, particle filtering to update the battery aging model parameters and Gaussian process regression (GPR) to fit the reconstructed components, are used respectively to further learn the long-term and local fluctuation parts of the battery capacity series. In the prediction stage, the prediction results of the two components are combined to obtain the predicted value of the future capacity of the battery and the uncertainty quantification of its RUL. Finally, the proposed hybrid model is validated on a battery dataset at different temperatures and experimental conditions, as a result, the RUL prediction method is shown to possess favorable prediction accuracy, good stability, and reliable uncertainty management capability.