Reliability of lithium-ion (Li-ion) rechargeable batteries has been recognized as of high importance from a broad range of stakeholders, including battery manufacturers, manufacturers of battery-powered devices, regulatory agencies, researchers, and the public. Assessing the current and future health of Li-ion batteries is essential to ensure the batteries operate safely and reliably throughout their lifetime. This paper presents a new data-driven approach for prediction of battery remaining useful life (RUL) in the presence of corruptions (or errors) in capacity features. The approach leverages bilinear kernel regression to build a nonlinear mapping between the capacity feature space and the RUL state space. Specific innovations of the approach include: i) a general framework for robust sparse prognostics that effectively incorporates sparsity into kernel regression and implicitly compensates for errors in capacity features; and ii) two numerical procedures for error estimation that efficiently derives optimal values of the regression model parameters. Results of 10 years’ continuous cycling test on Li-ion prismatic cells suggest that the proposed approach achieves robust RUL prediction despite random noise in the capacity features.