An implantable medical device, such as an implantable pulse generator (IPG) used with a spinal cord stimulation (SCS) system, includes a rechargeable lithiumion battery having an anode electrode with a substrate made substantially from titanium. Such battery construction allows the rechargeable battery to be discharged down to zero volts without damage to the battery. The implantable medical device includes battery charging and protection circuitry that controls the charging of the battery so as to assure its reliable and safe operation. A multi-rate charge algorithm is employed that minimizes charging time while ensuring the battery cell is safely charged. Fast charging occurs at safer lower battery voltages (e.g., battery voltage above about 2.5 V), and slower charging occurs when the battery nears full charge higher battery voltages (e.g., above about 4.0 V). When potentially less-than-safe very low voltages are encountered (e.g., less than 2.5 V), then very slow (trickle) charging occurs to bring the battery voltage back up to the safer voltage levels where more rapid charging can safely occur. The battery charging and protection circuitry also continuously monitors the battery voltage and current. If the battery operates outside of a predetermined range of voltage or current, the battery protection circuitry disconnects the battery from the particular fault, i.e. charging circuitry or load circuits.