Goddard, who is also a New Zealand High Court judge, admitted after her appointment that she was unfamiliar with British law. She was selected by former Home Secretary - now Prime Minister - Theresa May in February last year.
She is the third chair of the inquiry to resign, after Baroness Butler-Sloss and Fiona Woolf.
Goddard said she had found the job a "struggle" and missed her "beloved family" in New Zealand.
"The conduct of any public inquiry is not an easy task, let alone one of the magnitude of this. Compounding the many difficulties was its legacy of failure which has been very hard to shake off ... it would have been better to have started completely afresh."
Goddard had become one of Britain's highest-paid public servants with a 360,000 ($658,151) salary, a 110,000 ($201,101) accommodation allowance and regular free return flights to New Zealand for her and her family. After taking on the role she spent more than 70 days overseas, either on holiday or working abroad.
The inquiry into child abuse and the failures of institutions to protect children was set up in 2014 and is expected to last at least five years.
- Agencies