I have just downloaded R and Rstudio, both with latest version. Every time when i try to click on the Rstudio icon to launch it, it pops up this little window and it asking me to install rstudio again and again all the time. Anybody knows how can i fix this problem?
It might help if you posted a screen grab of the window. Also, you might try starting RStudio from a command line and see if any error messages are displayed.
I have already rstudio installed. I reinstalled and deleted both R and Rstudio several times and the problem remains.
Did you click the button to finish the installation?
of course I did. As i wrote before, I have it installed and finished on my machine and whenever I try to launch it, it pops up this window to download (which is already downloaded on my computer). I click yes and go through the installation again and keep all default settings until i click finish, and nothing happens after that. I have been trying 
many times, and sometimes i get a new app (rstudio), so I have like 3 different (rstudio) all are latest version.
It's a bit of a long-shot, but you can try uninstalling RStudio, then resetting its state as described here, then reinstalling RStudio. (Uninstall/reinstall does not by itself reset the state.)