"Ali Rida Fouad Hajj Hassan (22) was killed with three other Hezbollah fighters in the Qalamoun region," the source added.
In May, the armed party acknowledged for the first time that it has sent fighters to support the Syrian troops in the battles against the rebels.
According to the source, the bodies of the fighters were not brought back yet to Lebanon.
President Bashar Assad's forces launched an offensive this month in the rugged Qalamoun region north of the capital and along the Lebanese border in an attempt to prevent the flow of fighters from its western neighbor.