Is there a direct way for me as an Admin to update one of my user's email?

[Bernard Perlas]

One of my users is now using a new email, and no longer has access to the old email is there a way for me to change his email or does he have to change it? 

[Danny Flynn]

Are you an Organization Admin?  ...and is this a managed account?  

If so, you should be able to make the change by following these steps:  Make changes to a managed user account

If the user is not a managed account, they will need to make the change.