I downloaded unity 5.1.03f 64bit editor for windows and installed it. Installation is error free.When finished the installation, When tring to open the unity, the following error is showing. How can I fix this?

Try updating your Windows.

I found this answer in one of old unity question.See if this works(http://answers.unity3d.com/questions/510681/unity-editor-has-stopped-working.html)

Right Click Shortcut of Unity on Desktop

go to properties.

add this " -force-d3d11 " to the target ("C:\Program Files (x86)\Unity\Editor\Unity.exe" )

It should look something like this:

"C:\Program Files (x86)\Unity\Editor\Unity.exe" -force-d3d11

in some cases try -force-opengl instead of -force-d3d11

Note however that then you will be stuck using opengl, not 11.

Often the solution to this problem on Windows8 is to restore your system (control panels -> restore) to the previous day ... it can help.

Try to restart the computer and open Unity again. If it still doesn't work, make sure you have enough space on the installation drive (probably C: ). If still not working, consider upgrading or installing .NET Framework. But probably you need to update Windows with the latest Service Packs and system updates. Also, make sure the latest graphic drivers are installed.