Choudary was found guilty at the Old Bailey in August of backing IS in an oath of allegiance published online and was jailed for five-and-a-half years.
The Judicial Office has confirmed the 49-year-old has now applied for permission to challenge the verdict.
Police say Choudary's followers carried out attacks in the UK and abroad.
But they said they had been unable to act for many years as Choudary - a former solicitor and married father of five - had stayed "just within the law".
Choudary, of Ilford, east London, was convicted alongside and Mizanur Rahman, 33, from Palmers Green, north London, of an offence contrary to section 12 of the Terrorism Act 2000.
Their trial heard the pair also used speeches to urge support for IS, which is also known as Daesh, after it declared a caliphate in the summer of 2014.
Choudary was once the spokesman for al-Muhajiroun, an organisation banned in the UK.
The application for permission to appeal was lodged in early September and is being processed before being heard by a single judge.
Radical preacher Anjem Choudary is attempting to launch an appeal against his conviction for inviting support for the so-called Islamic State group.