On Ununtu by default you will not have an option to set root password, the root user have created while installation. The root user is rarely necessary, if you need to do as administrator can use sudo or gksudo. Also set password of root user using the below options commands,

Option 1:

Open your terminal.

use sudo with that the options are -s or -i

# sudo -i
or
# sudo -s


[sudo] password for demo:(enter your user password)

# passwd

Enter New Unix password: (enter your root password)

Retype new unix password: (reenter your root password)

passwd: password updated successfully


Now, the root user password has set successfully.

Option 2:

The below commands for demo represents system username. You can replace demo with your system username.
 
# sudo passwd root


[sudo] password for demo: (enter your user password)

Enter New Unix password: (enter your root password)

Retype new unix password: (reenter your root password)

passwd: password updated successfully

3.Password has set successfully to root.