Before root Xiaomi Redmi Note 3 make sure the Bootloader is unlocked. If locked read the how to unlock bootloader first. Next you need to flash TWRP recovery to the Redmi Note 3. The last download SuperSU zip file and install it to the phone.
We assume that the phone bootloader is unlocked. Now, how to flash TWRP recovery to the phone:
Download TWRP Recovery image file from http://www.smiui.net/files/TWRP_redminote3_patchedBySebsch1991.img
Fastboot.exe file, the file in the Unlocking Software ZIP ( or download it at http://www.smiui.net/files/MiFlashUnlock_hennessy.zip )
Flashing TWRP Recovery Redmi Note 3:
- Reboot the Phone to Fastboot Mode ( press and hold volume down key and power key for a few seconds, then release all keys when bootloader mode appears )
- Connect the Phone to computer via USB cable
- Run a windows terminal in the directory where the patched TWRP Image and Fastboot exe is located type “fastboot flash recovery TWRP_redminote3_patchedBySebsch1991.img”
- Wait for the process to finish type “fastboot reboot”
- After the system comes up you can reboot to Recovery mode ( press Volume up key and Power key for a few seconds, then release all keys when Mi logo appears )
- Now the phone fully working TWRP Recovery
When finished flashing TWRP Recovery, now How to root the Redmi Note 3:
- Download the SuperSU Zip-File at https://download.chainfire.eu/696/supersu/
- Copy the SuperSU zip file to the Phone
- Reboot the Phone to Recovery Mode ( press Volume up key and Power key for a few seconds, then release all keys when Mi logo appears )
- Select “INSTALL”
- Select the downloaded SuperSU Zip-File
- Wait for installation process to finish
- Reboot the phone
- Now the Xiaomi RedMi Note 3 Rooted!
Source and troubleshooting pls visit :
http://xiaomi.eu/community/threads/ultimate-guide-how-to-unlock-bootloader-root-and-flash-recovery-on-redmi-note-3.29213/