That's not problem with gnome, linux distributions like fedora, ubuntu doesn't allow you to login as root.
The developers decided that we should not be allowed to try and be smart enough to decide for ourselves that we do not want to log in as root in gnome/kde.
Type your root password. Next, make a backup of /etc/pam.d/gdm, enter:
cp /etc/pam.d/gdm /root
Now open /etc/pam.d/gdm using gedit or vi text editor, enter:
Alternatively, you can do everything in a one command:
su -c 'gedit /etc/pam.d/gdm'
Find line that read as follows:
auth required pam_succeed_if.so user != root quiet
Remove or comment out line by prefixing #.
# auth required pam_succeed_if.so user != root quiet
Save and close the file. Logout from terminal and from GUI itself. Now you should be able login as root user using GDM GUI login manager.