An apparatus and method for controlling the horizontal oscillation of an edge dam of a twin roll strip caster is provided. The apparatus includes an oscillation unit which horizontally oscillates an oscillation plate in accordance with an oscillation waveform so that an edge dam refractory coupled to the oscillation plate horizontally oscillates, a servo valve which outputs the oscillation waveform to the oscillation unit, and a control unit which applies the oscillation waveform to the servo valve, thus controlling the horizontal oscillation of the oscillation unit. The amplitude, frequency and waveform of the oscillation are variably controlled depending on casting conditions. The edge dam horizontally oscillates, using the servo valve and a hydraulic cylinder, thus rapidly removing edge skull and suppressing the generation and growth of skull, thereby preventing a casting roll or edge dam from being damaged.