Gdebi is an offline installer. If your computer isn't Internet connected, and you need to download your .deb files an another computer and then transfer them to yours, you can do so.
You can find .deb files at http://packages.linuxmint.com/
. For the latter you need to know the release name of the Ubuntu package base used on your Linux Mint release; you can see that here: http://www.linuxmint.com/oldreleases.php
You can also use Synaptic on your own computer, and create a download script for the packages you wish to install. It will include all the missing dependencies for download also. Though this might not work if you don't from time to time update the packages index files on your computer (as Synaptic will then create a download script for obsoleted versions of packages).