The children's puppet aired Sunday, part of series called "Exceptionals."
In the episode, Bush, a hand-held puppet dressed in a green uniform and wearing boxing gloves, is shown talking to a Palestinian child.
The child, with tears in his voice, accuses Bush of killing his father in Iraq, his mother in Lebanon and his brothers and sisters in Gaza with the assistance of the Israelis.
The Islamic Hamas overran Gaza last June. Israel, the U.S. and EU consider it a terror group. Hamas charges the U.S. with backing Israeli attacks.
The unnamed child tells Bush: "Your are a criminal. You deprived me of everything."
The child says, "I have to take my revenge with this sword of Islam."
Bush, in a panic, pleads for his life. "I repent. Don't kill me."
He invites the child for talks in the White House. But the child counters that the White House has been turned into a mosque, and "impure Bush" can't enter it. Then the child stabs him to death.
In a previous Hamas production, a Mickey-Mouse lookalike preached against Israel and the United States and urged Palestinian children to fight them.