► A capacity fade model for lithium-ion batteries is proposed based on experimental data analysis. ► The model parameters are estimated and updated at each cycle using a Bayesian approach. ► The state of health and the remaining useful life of lithium-ion batteries can be accurately predicted by the proposed model with tuned parameters. ► As more data are used to update the model, the accuracy and precision of the prediction improve. A new method for state of health (SOH) and remaining useful life (RUL) estimations for lithium-ion batteries using Dempster–Shafer theory (DST) and the Bayesian Monte Carlo (BMC) method is proposed. In this work, an empirical model based on the physical degradation behavior of lithium-ion batteries is developed. Model parameters are initialized by combining sets of training data based on DST. BMC is then used to update the model parameters and predict the RUL based on available data through battery capacity monitoring. As more data become available, the accuracy of the model in predicting RUL improves. Two case studies demonstrating this approach are presented.