The Australian Human Rights Commission says it has closed the file on Mr Leak's August cartoon - which depicted a neglectful indigenous parent - after Perth woman Melissa Dinnison decided not to proceed.

Ms Dinnison made an online complaint under section 18C of the Racial Discrimination Act, claiming she had experienced racial hatred as a result of the cartoon. But the commission on Friday wrote to Leak's employer, The Australian, to inform them controversial case would not go ahead.

Mr Leak accused Ms Dinnison of making her complaint "very flippantly and recklessly".

"It shows what a farcical process this is. I've got News Corp backing me legally. But if I was a private citizen, this would have cost me an absolute fortune," he told The Australian.

"She has put me through a month or so of incredible stress. She never met me, she doesn't have to justify anything she does. No one asked her any questions and it doesn't cost her a cent. As a consequence my life has been thrown into utter chaos. And at time when it just happens to suit her, she just decides this could turn into a bit of a hassle, so she can withdraw it."

The case helped fuel calls from free speech advocates and some in the Turnbull government for changes to 18C.

The government confirmed this week Parliament's human rights committee will examine freedom of speech, including possible changes to 18C and the commission's complaints-handling process.

As it stands, the law makes it unlawful to "offend, insult, humiliate or intimidate" on the basis of race.

Government backbencher Eric Abetz said the complainant's decision to drop the case was cold comfort.

"Regardless of the outcome of this case or the QUT students case, the punishment has been in the process which has seen people fork out tens of thousands of dollars and have their reputation trashed while the Human Rights Commission bumbles along denying Australians natural justice," he said.

"Mr Leak was fortunate to have the backing of News Limited. Any other Australian who didn't have that kind of backing would have been monstered into submission."

Former prime minister Tony Abbott blasted the commission this week, calling it "crook" and describing members as the "thought police".

The cartoon showed an indigenous police officer presenting a boy to his father and saying: "You'll have to sit down and talk to your son about personal responsibility."

"Yeah righto, what's his name then?" the father replies.