The dynamic behaviors of underwater bubbles and arcs are critical to welding processes and weld quality in underwater wet flux-cored arc welding. In this study, bubble evolution promoted by an arc plasma and flux decomposition was simulated using hydrodynamic equations. The influence of water on bubble and arc behavior was considered with regard to ionization of hydrogen in the arc, gas-liquid interfacial surface tension, and the absolute pressure. The interface between the water and bubble was determined via the volume of fluid and level-set methods. Physical parameters of mixed gas or plasma in the bubble were calculated by mass weighted average method based on the values of pure gas or plasma. The arc and bubble temperature distributions, fluid flows, and internal pressures were analyzed to reveal heat and mass transfer in the arc. The cycle of arc bubble evolution was about 0.056-0.063 s in calculation. The velocity of arc plasma could reach up to 500 m/s, which was one of the major factors to influence the arc bubble behaviors. Experiments were performed and the results showed that the simulated bubble shape, growth cycle, and evolution process agree well with the experimental data.