Is that possible to make a single article as homepage, but not connected with any menu item?
I'm using Joomla 1.7
No that is NOT technically possible - Joomla is menu driven.
But you could create a Menu Item (of type Article -> Single Article View) set it to be the default item (so it is your home page) and set the main menu module to not be shown on that page (if that is what you are trying to achieve).
The other option - is to create a new menu - for example called 'hidden'. Add your new menu item to this menu, and don't even have a module for this menu.
One or other of these options should do what you need.