When i was playing my psp it suddenly turned off so i thought it is out of charge.i charged it then i saw it was full charge so i unplug the charger when i unplug the charger it suddenly turned off.It only works if my charger is plugged in the psp.

It sounds like you have either a dead (broken) battery or your battery isn't making good contact with the motherboard.

Remove your battery and make sure there is nothing stuck in the terminal slots. Also make sure the metal contacts in the batter chamber of the PSP are clean. Then replace the battery.

Give it a little extra push on the back of the battery after you put it in near the battery terminals to make sure you get a solid connection.

If it still doesn't work then you may have a bad battery and will have to replace it. They can be found on ebay fairly cheap. (dont buy the $3 ones though they last about 10 minutes.)

There is still hope, try different chargers, try your charger on another psp. insert a fully charged battery. if all of that fails There may be a physical issue with your dc-jack or logic board. If you want to fix it yourself, You can get the part at psp Repair and there is a guide that shows you how to put in the part at psp Repair Guide.