I just did git init to initialize my folder as Git repository and then added a remote repository using git remote add origin URL. Now I want to remove this git remote add origin and add a new repository git remote add origin new-URL. How can I do it?

Instead of removing and re-adding, you can do this:

git remote set-url origin git://new.url.here

See this question: How to change the URI (URL) for a remote Git repository?

To remove remote use this:

git remote remove origin