As Lithium-ion batteries become the main power source in various electronics, it is important to predict the remaining useful life (RUL) of these batteries, in order to make the maintenance strategy and avoid serious consequences caused by the failure of power supply. With the convenience in fitting field measurements, the model based methods are widely used in RUL prediction for lithium-ion batteries. However, these predictions are usually unreliable because of incomplete uncertainty quantification. This paper proposes a model update method for the RUL prediction of lithium-ion battery based on the Bayesian simulator assessment theory. With an empirical degradation model, the method quantifies the uncertainties in model parameters, model form and measurements error. It infers the reality prediction to battery failure threshold with a combination of multiple uncertainties. The main innovation of the proposed method is that it doesn't only adjust the model parameters, but also the bias function which accounts for the model form uncertainty. And a modular Markov chain Monte Carlo method is employed to implement the model update with multiple uncertain parameters. As uncertainties are considered systematically in the inference process, it can provide a reliable RUL prediction. We demonstrate the predictive capability of the method by the real life cycle dataset of lithium-ion batteries from NASA.