Battery Charging Problem

If your Li-ion battery has a nominal voltage of 2.7 V, it is very likely that, while charging, this voltage go up. The data sheet would tell you exactly by how much. For example, a car battery that is 12 V rated, when fully charged reads some 13 -13.5V. While it is charged, the same battery would read 14-15V (depending on the charging current, the make and age of the battery etc).

Coming back to your battery, as a rule of thumb you would charge it with 1/10 to 1/7 of the capacity. So if it says that the battery is a 200mAh, use a charger that is, practically a current generator of about 20mA and that has an output (measured) of at least 4V. Now, for a small size Li-ion battery, charging with this current (or even larger in fast charging) might rise the temperature of the battery. The Li-ion chargers have a feature that, varies charging current as a function of temperature, voltage on the battery. You can get a Li-ion charger on ebay for a very low price, and disregard all my posting.

I think you will destroy the capacitor ( Condenser.) as the rating is too low for the supply.

{can the capacitor alone be used as a current source after charging}

Yes of course it can.

{Can some one suggest me a good circuit to charge a 2.7 volt Li-ion battery.}

If your battery is about 200mAH then the constant current source you have will be fine.