Saif al-Islam was not present in court and gave evidence via video link.
He is being held by a former rebel group from the town of Zintan that refuses to hand him over.
Former head of intelligence for the Gaddafi regime, Abdullah al-Senussi, is among those also facing the death penalty, as is former PM Baghdadi al-Mahmoudi.
Saif al-Islam is also wanted by the International Criminal Court on charges of war crimes and crimes against humanity.
Prosecutors say that he was part of his father`s plans to "quell, by all means, the civilian demonstrations against the Gaddafi regime".
Murder and kidnap
Saif al-Islam will be given the right to appeal the death sentence, according to the BBC`s John Simpson, who is in the Libyan capital, Tripoli.
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