How to remove /blog/ from permalink in WordPress MU

  1. I’m assuming that you have your permalinks as /%postname%/. Go to your blog and click on any post. You will notice the blog slug.
  2. Update the Permalink Structure.
    Go to Network Admin » Sites » Move cursor over the main site name(/) » Edit » Settings » Scroll down to Permalink Structure and update it to /%postname%/ and click on Save at the bottom of the page.
    Go to your blog and click on any post, you will notice a 404 – page not found error. This is because the above step only updates permalinks.
  3. Update rewrite rules.
    Go to Site » move cursor on main site name(/) » Dashboard » Settings » Permalink. Notice Custom Structure. You will see that blog/ is outside the textbox and %postname%/ appears in the textbox. Do not edit or save anything on this page.
    What happens is when you visit this page, rewrite rules gets changed automatically.

Link: How To Remove The /blog/ slug From The Permalinks(URL) in WordPress Multisite Installation Without A Plugin