State-of-health prediction of lithium-ion batteries has been one of the popular research subjects in recent years. Accurate state-of-health prediction has an especially significant role for battery management systems. This study combines the empirical mode decomposition and bidirectional gated recurrent unit neural network optimized by slime mould optimization algorithm to develop the state-of-health prediction model. First, to deal with the short-term capacity regeneration characteristics and the long-term degradation trend in state-of-health curve, the original battery state-of-health sequence is decomposed into some intrinsic mode functions and one residual sequence by using the empirical mode decomposition. Then, slime mould algorithm is used to automatically find the best hyperparameters of the bidirectional gated recurrent unit model. Finally, the bidirectional gated recurrent unit model is established to predict the state-of-health of lithium-ion batteries. The experimental results show that the proposed state-of-health prediction method always exhibit great accuracy both for the LiCoO2 battery datasets from the Center for Advanced Life Cycle Engineering and for the LiNCM battery datasets in our own laboratory. Furthermore, for the same type of batteries, the offline established prediction model does not need to be retrained. All these indicate that this combined model has high robustness, excellent universality, and superb practicality.