From Tools > Clear Recent History and from Options > Privacy > Clear history... > Settings, you can clear form and search history.

From the bookmarks window, you can get a complete list of browsing history and manually delete all the Google items.

Do you mean the search history of the Google search bar on the Navigation Toolbar or the search bar on the Google web page or the search bar on the about:home page?

Also make sure that you do not get confused by the suggestions.

• https://support.mozilla.org/kb/Search+suggestions