Glitter, 61, whose real name is Paul Francis Gadd, was found guilty of committing obscene acts with a 10-year-old girl and an 11-year-old girl at his rented seaside villa in southern Vung Tau last year. He was convicted and sentenced on March 3 by a court in Vung Tau province.
"He told me he was innocent so he has to appeal to clear this matter," attorney Le Thanh Kinh said.
Kinh said he met with Glitter at Phuoc Co prison on Wednesday and that his client signed the appeal petition, which will be forwarded to the appeals court in Ho Chi Minh City.
Glitter has maintained his innocence throughout the case, and threw the court into disarray when, after being sentenced to three years in prison, he began shouting out his denials as police escorted him from the courthouse.
In its verdict, the court cited graphic testimony from the girls that Glitter had fondled and molested them many times in his villa and in nearby hotels.
The court said Glitter would be deported from Vietnam to Britain after serving his sentence. He was also ordered to pay compensation of 5 million dong (US$320; euro266) to each girl's family and court fees.
Glitter would be eligible for parole in November, a year after he was originally detained at Ho Chi Minh City's airport while trying to leave the country.
Kinh said his client appeared to be in good spirits during their hour-long meeting.
"Now he's OK. During the sentencing, he did not look good, but now he is OK. Yesterday, he was joking with me," Kinh said.
An appeals trial would likely not be set until three or four months from now, he said.