"The IS today stoned to death a man that it said was gay," the Syrian Observatory for Human Rights said, adding that the victim was around 20 years old.
He was killed in Mayadeen in the eastern province of Deir Ezzor, near the border with Iraq.
The Britain-based Observatory said IS claimed it found videos on his mobile phone showing him "practising indecent acts with males".
In a separate incident on Tuesday, an 18-year-old was also stoned to death in Deir Ezzor city after the group said he was gay, the Observatory said.
Activists on social media said that the dead men were opponents of IS and that the group had used the allegation as a pretext to kill them.
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The United Nations said this month the IS had carried out several executions by stoning of women in Syria it accused of adultery.
The jihadists proclaimed a "caliphate" in June after seizing swathes of Iraq and Syria.
Activists say IS carries out regular public executions -- often beheadings -- in areas it controls.