1. Log into your family site
2. Hover over the 'Family tree' tab and go to 'My photos’:
3. Click on the album you would like to delete, and then click on the icon next to the album’s title.
4. Select ‘Delete album’.
Please note, the media items in the album still won't be deleted and will remain in your family site's Photos library.
For instructions on how to delete photos from your family site, see: How do I delete a photo from an online album?