Perth woman Donna Nelson, 59, was handed a six-year sentence in December 2024 for bringing two kilograms of methamphetamine into Japan in January 2023.
In September, she lost an appeal against the conviction in Tokyo's High Court and had until Friday to launch another in the Supreme Court.
But her daughter Ashlee Charles confirmed Nelson wouldn't be doing so.
"Mum's ending the fight against her conviction and she will be applying for the international transfer of prisoner process (to serve her sentence)," Ms Charles told AAP.
"We came to this decision because we just want our mum home where she is close enough for regular visits."
Nelson was arrested at Japan's Narita International Airport, near Tokyo, after customs officials found the drugs hidden under the false bottom of a suitcase.
The Aboriginal community leader had told the court she was unaware of the drugs and she was carrying the suitcase for a man she hoped to marry.
The man called Kelly, who she met online in 2020, told her he was the Nigerian owner of a fashion business.
In 2023, he paid her to travel to Japan via Laos, and asked her to collect dress samples from an acquaintance in the Southeast Asian country.
She was supposed to meet him in Japan but he never showed up.
Nelson's defence lawyers had argued she was a romance scam victim with no awareness or intent of drug trafficking for profit in the recent appeal.
The judge said Nelson was fully capable and had time to think and realise that something was wrong with the man's request.
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