A 23-year-old American of Pakistani origin has been found guilty of supporting terrorism by attending an al-Qaeda training camp in Pakistan.
Hamid Hayat was arrested with his father in June 2005
Hamid Hayat was also convicted, by a court in California, of three counts of lying to the FBI.
He faces up to 39 years in jail when he is sentenced in June.
Hours earlier, a separate jury in his father Umer's trial failed to agree on charges he lied to the FBI about his son's visit. A mistrial was declared.
Defence and prosecution lawyers are due to meet on 5 May to decide whether a re-trial should be carried out.
Both Umer Hayat, a 48-year-old ice cream vendor in Lodi, California, and his son were arrested last June.
The charge sheet filed in Sacramento alleged that Hamid Hayat provided support for terrorist acts between March 2003 and June 2005.
Assistant US Attorney Laura Ferris argued during the trial that Mr Hayat had trained with militants in Pakistan and planned to carry out attacks in the US.
She described him as a young man with a "jihadi heart and a jihadi mind".
But defence lawyer Wazhma Mojaddidi argued there was no evidence to back up such claims, and vowed to seek a new trial.
"Hamid Hayat never attended a terrorist training camp. This fight is not over," she said.
Defence lawyers had argued that Mr Hayat's confessions during FBI interviews, that he had trained in an al-Qaeda camp for about six months in 2003-2004, were made under duress.
The same argument was made in the trial of Umer Hayat, which was heard by a different jury to that of his son.
Court documents said Umer Hayat originally told FBI agents his son had nothing to do with the terror camps, but later confessed he had paid for his travel to Pakistan and to undergo "jihadi training".