The defendants, sentenced to at least two years in prison, also include one Yemeni citizen, while the rest are all Saudi nationals, said the official SPA news agency.
The US citizen, who was not named, was jailed for 17 years.
The special court found them guilty of "forming a terrorist cell that plotted attacks against oil pipelines... and some citizens" and disobeying the kingdom's rulers, with some of them travelling to join wars abroad.
Members of the group had also "attempted to carry out a terrorist attack in the kingdom (of Saudi Arabia) and Bahrain," site of a Shiite-led uprising against the Sunni regime.
Massive protests lasted one month until a nationwide crackdown which was backed by Saudi-led Gulf forces that rolled into Bahrain in support of the ruling Al-Khalifa family in March 2011.
The defendants were also convicted of training for armed combat and possessing weapons and ammunition "in a bid to undermine security" as well as "financing terrorism," said SPA.
Their identities were not disclosed and it was unclear if their trial was linked to those of dozens accused of belonging to Al-Qaeda or of involvement in the wave of unrest unleashed by extremists in 2003.
In 2011, Riyadh set up specialised terrorism courts to try the extremist who include Saudis and foreigners.