If it’s the 2000 series (PSP Slim), then yes. Connect your PSP system to an available USB port on your computer. Turn on your PSP, then under “Settings“, select “USB Connection”. Your PSP should connect to your computer and start charging. It may take awhile, but it will charge it all the way. Hold the display button (The button with the rectangular shape at the bottom of your PSP) until the screen goes black. This will speed up the charging process and is a good method of prolonging battery life when listening to music or other things.
If that doesn’t work, try looking for an adapter lying around your house that matches the volt numbers. The PSP takes 5V. Most portable CD players use 5V adapters and are usually the same size as needed for the PSP. I suggest using an adapter that matches the volt number and fits without trouble. If the orange light doesn’t come on or the PSP acts weird after charging, I’d stop using the adapter. Ask me any questions if you have any. ;)