An Adelaide man who posted videos on Facebook encouraging the killing of Jewish people has been found not guilty because he was suffering from paranoid schizophrenia at the time.

The 52-year-old man from Flinders Park in Adelaide's west, whose name was suppressed, became the first Australian to be charged with advocating terrorism in December 2016.

He was arrested by Australian Federal Police following information received through the National Security Hotline.

The charges related to four videos the man posted on Facebook between July 2015 and January 2016, where he encouraged others to kill Israeli soldiers and Jewish people.

During the videos he speaks in Arabic, referring to himself as a commander with Hezbollah and can be seen brandishing a large kitchen knife and a tomahawk.

In one of the videos, which had been viewed more than 19,000 times, he calls for Jewish people to be attacked with knives.

"When you come to a Jew, any Jew, even an old one who looks humble, pretending to be humble ... strike him in the head, when you strike him in the head, he will not even sneeze, he will die."

In another video he calls for the death of the president of the Palestinian National Authority, Mahmoud Abbas.

Police seized the knife, tomahawk and a chainsaw from his home.

The jury was told there was no dispute between the prosecution and defence that the man advocated terrorism and they agreed he was mentally impaired at the time.

"The defendant admits that his conduct in each of the videos, which will be played, amounts to a terrorist act," Commonwealth Prosecutor Anne Barnett said.

Ms Barnett said the trial, which went for fewer than two hours, was somewhat unusual because no witnesses would be called to give evidence.

Defence lawyer Edward Jolly said the two forensic psychiatrists who assessed his client agreed he was suffering from paranoid schizophrenia at the time.

As the man was charged under Commonwealth law, a jury had to determine whether or not he was mentally impaired at the time of the offending, whereas under state law, the finding can be made by a judge.

The man, who has been in custody since his arrest, will face court again on Thursday.