Boot the computer and select your Mint OS in the Grub menu, but do not press ENTER - instead press e (for EDIT).
Arrow down to the line that starts with "linux"
It will look something like this: linux /boot/vmlinuz-3.16.0-38-generic root=UUID=b1bde976-50e2-4c32-a760-17b091b4202f ro quiet splash $vt_handoff
Go to the end of that line. Delete the words "quiet splash $vt_handoff" if that is there, and put: rw init=/bin/bash
Then press F10 to boot. That will boot to a root shell.
Enter: passwd yourusername (whatever your user name is...)
Press Enter. It will request the new password (twice).
Note: when you type your new password, it will not display on the screen (for security reasons).
When complete, press Ctrl+Alt+Delete to reboot.