Lithium-ion batteries (LIBs), as crucial components of energy storage systems, ensuring their health status is of great importance. In this paper, a new method based on data-driven is proposed to estimate the state of health (SOH) and predict the remaining useful life (RUL) of lithium-ion batteries. Through correlation analysis, the health indicator (HI) selects the voltage value corresponding to the peak in the incremental capacity data. An ensemble deep random vector functional link (edRVFL) network is employed to excavate the relationship between health indicators and the state of health. Subsequently, another same network combined with a nonlinear autoregressive (NAR) structure is applied to predict the remaining useful life. The effectiveness of the proposed method was validated using a publicly available dataset.