You can use iTunes to exit recovery mode. This method will erase everything on the iPhone, but a backup will be created during the restore process, allowing you to recover your data. Now follow the steps below to fix [http://goo.gl/vHosbe|iPhone stuck on recovery mode] problem:
(1) Connect your iPhone to your computer and run iTunes on your computer.
(2) Select your iPhone from the list of buttons at the top of iTunes, then click the "Restore" button.
(3) Wait for the backup and restore process to complete, then "restore from backup" in iTunes after the phone has been restored.