Alan Henning, a 47-year-old Briton who volunteered to help drive an aid convoy to Syria for Muslim charity Aid4Syria, was kidnapped 10 months ago.
"An audio file of Alan pleading for his life has just been received by me," his wife Barbara said in a statement released through Britain's Foreign Office.
"He went to Syria to help his Muslim friends deliver much needed aid."
"We are at a loss why those leading Islamic State cannot open their hearts and minds to the facts surrounding Alan's imprisonment and why they continue to threaten his life."
It was the family's second appeal since Henning, a father of two teenage children, was threatened in a video that showed the brutal killing of British aid worker David Haines earlier this month.
Barbara Henning said that her attempts to communicate with the IS group had been ignored, and that she had learned that Henning had been cleared by an Islamic law court.
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"I have been told that he has been to a Sharia Court and found innocent of being a spy and declared to be no threat," she said.
"I implore Islamic State to abide by the decisions of their own justice system. Please release Alan."
The appeal came after the release of a new video of another British hostage, freelance photojournalist John Cantlie, who first appeared last week in a video in which he announced he was being held captive by IS.
The new video is introduced as "Episode 1" in a series, and shows Cantlie criticising the actions of Western governments in a pre-prepared script.
On Tuesday the United States and Arab allies attacked jihadists within Syria in bomb and missile strikes, a turning point after years of reluctance from the West to intervene in Syria's civil war.
Following the strikes the brother-in-law of the kidnapped Henning said he feared the move could make it harder to find and rescue the hostage as militants fled attacks.
"They'll take him with them and no one will know where he is again," Colin Livesey told ITV News.