I have found others who have reported this issue. I have downloaded THREE TIMES from the official LibreOffice site the latest LibreOffice-x_win_x86.msi and every single time it fails to work on Windows 7. Every single time it says “This file could not be opened…” Simply saying “re-download the file” is not an answer since repeated downloads fails to fix it. What WOULD fix it would be providing an exe version of the suite for installation rather than your broken msi. I’m about to give up on LibreOffice as a result of this.
That probably means the download was corrupted on the first try. The solution is to Clear your browser’s cache. Alternatively, download from a different location.
Choose a mirror near you
http://download.documentfoundation.org/mirrors/all.html
There are no exe downloads. An msi is a Microsoft installer pack (so that is not the problem)
Hope this helps 
Have you try run the file with administrator rights?.
Right-click the file and select the option.