In Ubuntu 13.10 / 13.04 / 12.10 and Ubuntu 12.04, User defined login or GUI root login is disabled by default. You can enable the user defined login by modifying the lightdm configuration file. Once the manual login is enabled, then its easy to login as root in GUI.
To Enable Manual Login in Ubuntu 13.10 13.04 12.10 12.04
Open a Terminal run the following command, Issue the password for the user when prompted.
sudo sh -c 'echo "greeter-show-manual-login=true" >> /etc/lightdm/lightdm.conf'
Now set / change the password for the root user in your machine.
To set / change the root password in Ubuntu 13.10 13.04 12.10 12.04
Run the below command in the terminal to create a new password for the root user. Issue the password for the user, when prompted.
Enter the password twice. After creating the password, restart the system.
Now you can find the manual login option in the login list. Select Login and type user name as root and provide the root password which you have created. Check the screen shot.
Hope this will be helpful for you!!!