i have tried using session but session is for internet explorer only .
This is not true. Are you sure that you implemented sessions correctly?
That said, it is possible for two users to be logged in simultaneously with sessions. This is exploited by session hijacking and session fixation attacks.
The way that I would use is this:
From the point of successful login onwards, issue a new hash identifier on each page load.
This can be in the form of a cookie, or a session variable.
The current hash identifier for the user would be stored in the database, and the user might also be tracked with his/her database table user id (to ensure that hash collision is harmless).