The actor, who played Ron Weasley in the Harry Potter movies, is fighting previous ruling, which found HMRC was right to block a tax return of £1m.
In 2016, Grint tried to claim the tax back by using a change in accounting dates to avoid paying a higher tax rate on his earnings.
At the time Judge Barbara Mosadele found Grint had changed his accounting date so 20 months of income would be taxed in 2009/10, one year before the top tax rate rose from 40%to 50%.
She ruled he was not entitled to the refund as he had failed to give a valid reason for such change.
He has now taken his case to the Upper Tribunal, with his barrister Patrick Sooares claiming the previous judge used the wrong legal test in the ruling.
According to the Daily Mirror, HMRC is contesting the appeal, as it believes there was no error of law.
When discussing money with Radio Times magazine recently, he said, "I actually don't know how much I have. I couldn't even really guess.”
HMRC declined to comment.