This paper presents a hybrid approach for predicting the remaining useful life (RUL) and future capacity of lithium-ion batteries (LIBs) using an improved long short-term memory (LSTM) deep neural network with a gravitational search algorithm (GSA). The proposed method address the challenges of nonlinear and dynamic battery behavior, battery aging uncertainty, the requirement for optimal hyperparameters tuning, and the importance of maintaining safe and efficient battery operation. The RUL prediction uncertainty with a 95% confidence interval (CI) is also analyzed. The GSA algorithm optimizes the hyperparameters of the LSTM network to construct an optimal model. The method proposed in this work is evaluated based on the aging data from the NASA battery dataset, and its effectiveness is compared with that of BiLSTM, baseline gated recurrent unit (GRU), and baseline LSTM using various error metrics. The results demonstrate that the LSTM-GSA model outperforms other methods in the context of prediction accuracy, achieving a minimum RMSE of 1.04% and 1.15% for both battery cases. Overall, this research provides a promising solution for predicting RUL and the future capacity of LIBs with uncertainty, which is essential for ensuring the safe and efficient operation of energy storage systems.