This has nothing to do with the operating system.
You missed a step in securing the database. It's important that you follow all the steps, skipping nothing. It also depends on your version of Access.
Security FAQ
http://support.microsoft.com/?id=207793
Security Whitepaper
http://support.microsoft.com/?id=148555
Although the whitepaper is old, it contains information to help you understand security.
I've also outlined the detailed steps at
www.jmwild.com/AccessSecurity.htm

Signature
Joan Wild
Microsoft Access MVP
>I created a user level security for a database on a computer with Windows
> 2000 as an OS, and it works, when I access the database from a computer with
> Windows XP as an OS, it lets me without asking for a user name or a password.
> How can I fix that?
>
> Thank you in advance