Mac Air shutdown when im using it for 5 to 15mins without Power Adapter and just turn on again with Power adapter , althought batery is full

Hello hosseinmp,

Thanks for using Apple Support Communities.

To start troubleshooting this issue where your Mac is shutting down unexpectedly when not plugged in, I'd like you to please reset what's called the SMC. In order to reset the SMC, please follow the steps below.

On Mac notebooks with non-removable battery

Mac notebook computers that have a battery you should not remove include: MacBook Pro (Early 2009) and later, all models of MacBook Air, MacBook (Late 2009), and MacBook (Retina, 12-inch, Early 2015).

To reset the SMC:

1. Shut down the computer.
2. Plug in the MagSafe or USB-C power adapter to a power source and to your computer.
3. On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
4. Release all the keys and the power button at the same time.
5. Press the power button to turn on the computer.

On MagSafe power adapters, the LED might change states or temporarily turn off when you reset the SMC.

Resetting the System Management Controller (SMC) on your Mac - Apple Support

Take care.

Try Resetting the System Management Controller. When that fails to help, take the computer to an authorized service place.