There is no "Close Sprint" button on the Active Sprints page. I have check my permissions and I have jira-administrator. All issues in the sprint are closed.

[Josh Speerstra]

This is super old, but I just ran into this. Permissions were correct and we were all scratching our heads. It turned out there was another active sprint in the project. The "View" for the "Active Sprint" board was accounting for all the open sprints in the project. Therefore, changing the view to the sprint that you are looking for will allow you to close the sprint. 

[Nic Brough -Adaptavist-]

JIRA admins have administrative rights to administrate.  Not do everything (it's a poor security model)

Have you got "manage sprint" permissions in all the projects the board covers?