First thing you need to do is log in to your WordPress site and go to Settings » Discussion. Scroll down to the Avatars section and uncheck the box next to ‘Show Avatars’ option. You will need to click on the Save Changes button to store your settings.
That’s all you have successfully disabled Gravatar on your WordPress site. Your comments will not show user gravatars. You will also not see gravatars anywhere in WordPress admin area. User gravatars will not appear on Comments and Users screen, your gravatar from WordPress admin bar will also disappear.
Even though you have disabled gravatar on your WordPress site, you can still show them selectively if you need. For example, you can display gravatar in author info box, or display gravatar from user email anywhere on your site.