Check out this lithium ion charging circuit made without a dedicated charging IC.

This is a simple li-ion charger without a dedicated li-ion charger IC. This circuit can be used to efficiently and intelligently charge any single cell Li-ion battery pack like mobile battery, digicam battery, etc.

Features:

• Charging via mini-USB connector which is very common.
• Charging status display by LED
• Simple circuit by using opamp, resistor, and not by any complex dedicated IC or micro-controller.
• Charges completely drained (0V) battery packs.
• Max charging current 500mA(limited by USB supply), depending on battery.