I build a web application in asp.net 4.0,in which users are authenticated using Windows Authentication/ Active Directory membership provider.
This sounds like, there is no issue with implementation. Windows authentication is properly implemented and working.
user enter only URL on its machine ,if it is authenticated user than access my web application other wise redirected to longing page for anonymous user.
This is based on browser settings of client system.
For IE:
Tools -> Internet Options -> Security -> Local Intranet -> Custom Level (Security settings) -> User Authentication -> Logon -> "Automatic Logon with current username & password"<br />
This setting will do what you ask.