This paper presents a unique method for estimating the state of health and remaining life of Li-ion batteries by fusing Gaussian process regression and neural networks. Specifically, the original capacity data are decomposed using the advanced empirical mode decomposition method to obtain several intrinsic mode components and a residual, representing local capacity regeneration and global degradation, respectively. Global degradation is tracked using a bidirectional long-short-term memory neural network, and the regenerative component is captured using Gaussian process regression. Considering the sensitivity of Bi-LSTM to parameters, the particle swarm algorithm with random weight is used for parameter optimization. Results on the NASA battery dataset show that the proposed method does not exceed 1% error in early SOH and RUL predictions.