Sami al-Arian and three co-defendants of Palestinian descent were arrested in February 2003 on charges of raising money and providing support for the Islamic Jihad resistance group.
The US lists the group as a "terrorist organisation" responsible for the deaths of over 100 people in Israel, including two Americans.
"The evidence will show the Palestinian Islamic Jihad is one of the most deadly terrorist organisations on earth, dedicated to the elimination of Israel," Assistant US Attorney Walter Furr said in his opening statement on Monday in one of the highest-profile terrorism prosecutions in the US since the 11 September 2001 attacks.
The prosecutor added that al-Arian, 47, a computer science professor at the University of South Florida in Tampa until his arrest, was one of the Islamic Jihad's top leaders.
"For a time, he was maybe the most powerful man in the world in this organisation," Furr said.
The defendants have denied the charges and said they were being prosecuted because of their political support for Palestinians.
"There is no question Sami is innocent. He is a good man"
Al-Arian's attorney William Moffitt told jurors there was no evidence linking the defendants to attacks in Israel, and said al-Arian had simply been using his freedom of speech rights in support of the Palestinian cause.
The trial is expected to last at least six months and the prosecution has called hundreds of witnesses, many from Israel.
The four defendants face life in prison if convicted of the charges, which include conspiracy to commit murder, extortion, money laundering and providing support for foreign "terrorist organisations".
Outside the courthouse, al-Arian's wife Nahla told reporters: "There is no question Sami is innocent. He is a good man."
She spoke as about a dozen supporters of the defendants demonstrated on the pavement.