Arc discharge in water can generate extremely high voltage, which has great potentials to be used in DC fault protection. The voltage characteristic is closely related to the arc behaviors. However, due to the complexity of the gas-liquid mixed environment, the arc shape is difficult to be observed directly. In this letter, an observation device is specially designed and underwater arc motion with millisecond-scale duration is clearly photographed. The corresponding relationship between arc behaviors and its varied voltage is revealed. Besides, the random behaviors of underwater arc is controlled stably by applying external transverse magnetic field (ETMF). The enhanced cooling mechanism and the directional arc motion characteristics are discussed. It demonstrates that, fast elongation of arc column and continuous heat exchange between phase surfaces are the keys to realize rapid increase of underwater arc voltage.