gauravkothari23, I just want to back up what Audioguru is saying.
I have used a lot of Li-ion cells, often without protection circuits, and they stll make me nervous after years of using them.
Mis-charging a NiCd or NiMH, or even a lead-acid, is not very hazardous. Most likely you will just reduce the cell's life. Mis-charging, over-charging or over-discharging a Li-ion cell really is dangerous, and the cell can even explode long after you have charged it as the damage continues internally. This has happened to people, it's not just theory. The cells can go off like fireworks when abused!
You must use a charger designed for your battery, or a specialised Li-ion charger that can be adjusted to the exact voltage and capacity like Radio Control enthusiasts often use for charging their battery packs. You cannot/must not use a basic power supply, NiCd/NiMH charger, or anything else not specifically intended to charge your exact battery.
There are integrated circuits readily available to build your own charger. You can power the charger circut however you want.
The protection circuit in a commercial Li-ion cell is not intended to do your job of regulating the charge, or anything useful to you really. It's purely there to (hopefully) stop catastophic failure (explosion/fire) if the cell is mistreated. Even so, do not rely on it to do its job if you don't do yours.
Buy a proper charger, or study some dedicated ic charger circuits (search here to start) and make one, that's not rocket science as it's mostly done for you in the ic. But don't think you can simply improvise a charger like you can for a NiCd.