Using wp single login you can easily add the functionality to allow only single login per user.
This plugin will automatically logout the already logged in user when a user with the same login details tries to login from different browser or different computer. This plugin needs zero configuration to run. Just install it if you want single login functionality on your site.
This plugin uses wordpress Heartbit API which was implemented in version 3.6 in order to logout users in real time.
wp single login is a lighweight wordpress plugin which adds the functionality to allow single login per user.