A former Adelaide student found guilty of being a member of Islamic State (IS) has had her conviction overturned on appeal, despite the state's chief justice accepting she had pledged allegiance to the terror group.

Key points: Zainab Abdirahman-Khalif was found guilty of having Islamic State membership

Zainab Abdirahman-Khalif was found guilty of having Islamic State membership She was jailed but appealed against her conviction

She was jailed but appealed against her conviction The Court of Criminal Appeal on Thursday overturned the guilty verdict

Zainab Abdirahman-Khalif was convicted at trial of knowingly being a member of IS, which the Court of Criminal Appeal on Thursday overturned.

Ms Abdirahman-Khalif, who is now 24, was detained at Adelaide Airport in July 2016 trying to board a plane to Turkey with just hand luggage and $180, but released without charge.

In May 2017, she was again arrested and charged by Australian Federal Police with "knowingly being a member of a terrorist organisation".

During a three-week trial last year, the South Australian Supreme Court heard the former student had pledged allegiance to IS and had been communicating online with young female members of the terrorist organisation.

The court heard 378 audio files associated with IS were found on her phone, along with 125 videos from an IS media organisation, 62 of which contained extremist material, including vision of buildings being blown up, captives being executed and dead bodies on the ground.

In April, Supreme Court Justice David Peek jailed her for three years and imposed a non-parole period of two years and three months.

Zainab Abdirahman-Khalif has had her conviction overturned. ( Nine News )

Ms Abdirahman-Khalif then launched an appeal against her conviction.

Her legal team argued there was no evidence presented at trial about the organisational structure of IS and how a person might become a member and, therefore, no evidence that Ms Abdirahman-Khalif had taken steps to do so.

They also argued that the trial judge's summing up to the jury was unbalanced and failed to present the defence case.

'No evidence' to prove IS membership

Three judges presided over the appeal, Chief Justice Chris Kourakis, Justice Trish Kelly and Justice Greg Parker.

The chief justice said the evidence at trial supported an inference that Ms Abdirahman-Khalif was a supporter of IS, its extremist ideology and its terrorist activities.

"It also supported the inference that she intended to travel to Turkey to make contact with members or supporters of Islamic State in Turkey, with the intention of travelling into areas of Syria, Iraq and Turkey … for the purposes of either providing medical assistance to fighters and others or to marry an Islamic State fighter," he said.

Zainab Abdirahman-Khalif in custody before her conviction was overturned. ( ABC News )

However, Mr Kourakis said the prosecution did not produce evidence about IS's organisational structure or membership.

"No evidence was adduced on how members were recruited or selected, or of any process by which they were inducted and finally accepted into the organisation," he said.

"Other than references to [IS leader Abu Bakr] al-Baghdadi's autocratic rule and to several of his immediate subordinates, there was no evidence about Islamic State's decision-making processes or command structure.

"There was therefore no evidence against which to evaluate any connection between the proved conduct of the appellant, her communications, pledge of allegiance, singing and attempt to travel to Turkey, with formal or informal membership of Islamic State."

Justice Trish Kelly found that the appeal should be dismissed.

"The material tendered by the prosecution demonstrated the appellant's specific interest in, and commitment to, Islamic State," she said.

"The amount of material found on the appellant's phone demonstrated the appellant's wholehearted acceptance and adoption of the extremist beliefs of Islamic State.

"The whole of the evidence pointed overwhelmingly to the appellant's guilt of the charge."

But Justice Kourakis said there was a "dearth of evidence" or any clear criteria by which members of IS could be distinguished from the group's sympathisers.

"The evidence did not prove that the informal membership of Islamic State … included the wives of its fighters or the persons who nursed them," he said.

"Insofar as those wives and nurses were members of a broad class of the population governed by Islamic State who supports its rule, they were not an organisation as defined."

The chief justice's decision was supported by Justice Parker, which resulted in the appeal being upheld on a majority decision.

Family rejoices after conviction overturned

Ms Abdirahman-Khalif was embraced by her family in court, who were crying and expressing their relief, following the decision.

During the trial, the court heard Ms Abdirahman-Khalif lived in refugee camps in Kenya until she was 14 years old and moved to Australia with her family, who are of Somalian origin, in 2009.

She said her attempt to travel to Turkey on a one-way ticket in July 2016 was a last-minute decision to go on an innocent holiday.

Ms Abdirahman-Khalif left court through the front doors as her lawyer James Caldicott was addressing the media.

Her exit prompted a flurry of activity but she quickly got into a waiting car without making further comment.

Mr Caldicott said his client would now be focused on "reconnecting with the community" and felt "grateful" for the court's decision.

"Particularly now that it's over and the ordeal's over. But again, it's just about spending time with friends and family," he said.

"Emotions are running very high … obviously she's just going to have a quiet night in tonight."