Accurate estimation of the state-of-charge (SoC) and state-of-health (SoH) for an operating battery system, as a critical task for battery health management, greatly depends on the validity and generalizability of battery models. Due to the variability and uncertainties involved in battery design, manufacturing and operation, developing a generally applicable battery model remains as a grand challenge for battery health management. To eliminate the dependency of SoC and SoH estimation on battery physical models, this paper presents a generic data-driven approach that integrates an artificial neural network with a dual extended Kalman filter (DEKF) algorithm for lithium-ion battery health management. The artificial neural network is first trained offline to model the battery terminal voltages and the DEKF algorithm can then be employed online for SoC and SoH estimation, where voltage outputs from the trained artificial neural network model are used in DEKF state-space equations to replace the required battery models. The trained neural network model can be adaptively updated to account for the battery to battery variability, thus ensuring good SoC and SoH estimation accuracy. Experimental results are used to demonstrate the effectiveness of the developed model-free approach for battery health management.