A robot swing structure uses a swing bracket to be in combination with a curved rack, and a transmission gear of a power mechanism to be in engagement with the curved rack. Whereby, when a first end of the curved rack is positioned at the transmission gear, the curved rack and swing bracket are allowed to be swung to incline downward (as if the robot head lowers or bows); when a second end of the curved rack is positioned at the transmission gear, the curved rack and swing bracket are allowed to be in a transverse state; and when a stop section of the curved rack is positioned at the transmission gear, the curved rack and swing bracket are allowed to be in a upright state, thereby making the curved rack and swing bracket to have three swing stopping states.