1. Install the ROM Manager on your LG Optimus Black P970. Get it from Android Marketplace Location, then install the clockwork mod recovery.
2. Connect your LG Optimus Black P970 to your PC employing the USB information cable. Copy the “LG Optimus Black P970_4.2 Jelly Bean.zip” file you downloaded to the SD memory card.
3. Restart your device in the recovery mode using ROM Manager. As soon as in Recovery Mode, go to ROM Manager and select backup / restore to back-up your information.
4. From the Recovery Menu do a total data erase (including Delvik Cache). When completed, go back to Recovery Principal Menu and choose Flash ROM from SD Card. Navigate the location you copied the ”LG Optimus Black P970_4.2 Jelly Bean.zip” file and follow the directions for installing Android 4.2 Jelly Bean on your LG Optimus Black P970. As soon as the installation is over, just reboot your LG Optimus Black P970 device, and here you go, you’ve just upgraded it to the new Android 4.2 Jelly Bean
Note : Here Is Link To Download the ROM/Zip File :