Judge Andrew Nicol ruled last November that Depp had violently assaulted his ex-wife Amber Heard during their tempestuous five-year relationship, at times putting her in fear for her life.
That decision came after three weeks of hearings where the court heard claims and counter-claims from Depp, 57, and Heard, 34, about violent outbursts which each accused the other of committing.
On Thursday, Depp's lawyers went to the Court of Appeal for permission to challenge the findings and in a written submission said "The judgment is plainly wrong and the consequential decision in favor of the respondents is manifestly unsafe."
Depp, star of films including "Pirates of the Caribbean" and "Edward Scissorhands," had gone to the London court to sue The Sun newspaper and one of its journalists over an article that stated he had been violent towards Heard.
Following Nicol's verdict, seen as being highly damaging to his career, Depp was asked to leave the "Fantastic Beasts" franchise, the movie spin-offs from the "Harry Potter" books and films.