To safeguard the security and dependability of battery management systems (BMS), it is essential to provide reliable forecasts of battery capacity and remaining useful life (RUL). However, most of the current prediction methods use the measurement data directly to carry out prediction work, which ignores the objective measurement noise and capacity increase during the aging process of batteries. In this study, an integrated prediction method is introduced to highlight the prediction of lithium-ion battery capacity and RUL. This approach incorporates several techniques, including variational modal decomposition (VMD) with entropy detection, a double Gaussian model, and a gated recurrent unit neural network (GRU NN). Specifically, the PE−VMD algorithm is first utilized to perform a noise reduction process on the capacity data obtained from the measurements, and this results in a global degradation trend sequence and local fluctuation sequences. Afterward, the global degradation prediction model is established by employing the double Gaussian aging model proposed in this paper, and the local prediction models are built for each local fluctuation sequence by GRU NN. Lastly, the proposed hybrid prediction methodology is validated through battery capacity and RUL prediction studies on experimental data from three sources, and its accuracy is also compared with prediction algorithms from the recent related literature. Experimental results demonstrate that the proposed hybrid prediction method exhibits high precision in the predicting future capacity and RUL of lithium-ion batteries, along with strong robustness and predictive stability.