If you have multiple OS installed in your system, and you want to change the default operating system from the list of Grub2, here is an easiest solution, which doesn’t actually require any software but just an editor to do a bit changing.

Change Grub Menu / Boot Order

All you need to do is to have a sudo / root access to change a file. Open up the following file in any editor like gedit or in terminal using vim, having sudo / root access:

/etc/default/grub

Once opened, you can see a text GRUB_DEFAULT, having value as 0, GRUB_DEFAULT=0

All you need to do is to change the value of this variable GRUB_DEFAULT to the order number of the OS from the Grub2 list, which you see and choose at start, to select your OS.

Note that, the numbering starts from 0, for example, if you have 4 items in Grub2 Menu:

Ubuntu, with Linux 2.6.35-22-generic
Ubuntu, with Linux 2.6.35-22-generic (recovery mode)
Ubuntu, with Linux 3.0.0-17-generic (on /dev/sda1)
Ubuntu, with Linux 3.0.0-17-generic (recovery mode)

and you want the third item from the above list to be selected as default, which is:
Ubuntu, with Linux 3.0.0-17-generic (on /dev/sda1)

you need to set the value of GRUB_DEFAULT as:
GRUB_DEFAULT=2

After you save the file, open up the Terminal, and write the following command:
sudo update-grub

Once done, simple restart your OS and see if you have successfully changed the boot order menu of Grub2.

Still Having Problems?

If you are still having problems and are unable to change the menu order of Grub2, after applying the above changes, you might have been missing something here. As you have multiple of Operating Systems in your system, make sure that the changes are being done on the main Operating System, like the one you recently installed, or the one which is coming as Default selection on Grub2.

Hope the solution works.