This solution requires you to install Microsoft Office SharePoint Designer.
 - Go to "Site Actions" ==> "Site Settings"
 - Under Galleries, click on "Master Pages"
 - Select default.master and select "Edit in Microsoft Office SharePoint Designer".
 - In "Design" view locate "View All Site Content" on the left-hand-site navigation bar and click on it.
 - Go to "Code" view. You will see the following code highlighted:
 
<Sharepoint:SPSecurityTrimmedControl runat="server" PermissionsString="ViewFormPages">
 <div class="ms-quicklaunchheader">
  <SharePoint:SPLinkButton id="idNavLinkViewAll" runat="server" NavigateUrl="~site/_layouts/viewlsts.aspx" Text="<%$Resources:wss,quiklnch_allcontent%>" AccessKey="<%$Resources:wss,quiklnch_allcontent_AK%>"/>
 </div>
</SharePoint:SPSecurityTrimmedControl>
- Change the PermissionString attribute value of the Sharepoint:SPSecurityTrimmedControl XML element from ViewFormPages to BrowseDirectories.
 - Save the default.master. If you login as an anonymous user you will not see the "View All Site Content" link. However when authenticated you will see this option.
 
NOTE: The "BrowseDirectories" permission is common to both the "Members" and "Owners" group permission levels, but is not set for the "Limited Access" (anonymous users) permission level. See a complete list of the SPBasePermissions Enumeration here.

