follow the steps below 

1.Go to your IIS manager (type inetmgr in Run hit Enter)

2.Select and open the SharePoint web application in which you have this error

3.Double click on Authentication icon.
here you will see different types of authentication listed for your Web Application

4.In that list Right click on Anonymous Authentication and Enable it if its disabled

now try  opening site in SharePoint designer again

for more details you can check here http://support.microsoft.com/en-us/kb/2758431