Lord Tu'ivakano was in April handed a two year suspended sentence after he was found guilty of making a false statement so that two Chinese nationals could get a passport.
He was also convicted of possessing a firearm and ammunition without a licence.
Our correspondent, Kalafi Moala, said the former prime minister claims to have substantial new information.
"They're challenging that because they [claim to have] other new evidence or new witnesses that basically providing information that is contrary to what was presented at the case."
