Fast charging is critical for the application of lithium-ion batteries in electric vehicles. Conventional fast charging algorithms may shorten the cycle life of lithium-ion batteries and induce safety problems, such as internal short circuit caused by lithium deposition at the negative electrode. In this paper, a novel, non-destructive model-based fast charging algorithm is proposed. The fast charging algorithm is composed of two closed loops. The first loop includes an anode over-potential observer that can observe the status of lithium deposition online, whereas the second loop includes a feedback structure that can modify the current based on the observed status of lithium deposition. The charging algorithm enhances the charging current to maintain the observed anode over-potential near the preset threshold potential. Therefore, the fast charging algorithm can decrease the charging time while protecting the health of the battery. The fast charging algorithm is validated on a commercial large-format nickel cobalt manganese/graphite cell. The results showed that 96.8% of the battery capacity can be charged within 52min. The post-mortem observation of the surface of the negative electrode and degradation tests revealed that the fast charging algorithm proposed here protected the battery from lithium deposition.