I have written a project for my students organization. I would like to share it between many organizations and I want them to use it for free. So I thought that releasing the project on GPL licence (or other silimar). However I don't want that somebody use this project for commercial purpose for free. How should I license this project? Is there any license that is suitable for that? Or should I release two copies of my project on different licences?
You should consult a lawyer to get good legal advice.
However, that being said, GPL is a very common license for this type of scenario. It doesn't, explicitly, restrict commercial use, but it does require that any distribution include full source and full distribution rights under the GPL. This effectively excludes commercial use.
For commercial purposes, you can easily negotiate distribution under a second license, even one specific to that company.
My company has licensed software written at universities and distributed publicly under GPL in exactly this manner.
If you release under the GPL, no-one can use your code unless their project is also GPL-licensed.
You should probably license your project with 2 different licenses: a free software license and a commercial license.
I remember a nice article about how to choose a free software license depending on your goals.
In any case, consult a lawyer.
I Am Not A Lawyer. If its an app that runs over a network, such as a web app, you should also consider the AGPL since the GPL will not prevent people from running the application over a network and then refusing to release their modifications to people who use the application (over the network).
Technically, if you forbid commercial use, your software is not "Free Software". There are several "nonfree" licenses that do what you ask, there is a list at the FSF website, e,g. the University of Utah Public License. Note the harsh criticism that the Free Software Foundation has for this nonfree license.