Lithium-ion battery charging management has become an enabling technology towards a paradigm shift of electrified mobility. Fast charging is desired for convenience improvements but may excessively degrade battery's health or even cause safety issues. This paper proposes a novel algorithm to manage battery charging operations using a model-based control approach. Based on a fully coupled electrothermal model, the fast charging strategy is formulated as a linear-time-varying model predictive control problem, for the first time. Constraints are explicitly imposed to protect the battery from overcharging and overheating. To enable the state-feedback control, unmeasurable battery internal states including state-of-charge and core temperature are estimated via a nonlinear observer using noisy measurements of current, voltage, and surface temperature. Illustrative results demonstrate that the proposed approach is able to optimally balance time and temperature increase. In addition, it is shown from simulations that the model predictive control based charging algorithm appears promising for real-time implementation. (C) 2017 Elsevier Ltd. All rights reserved.