A model for a moderately deep underwater explosion bubble was developed in inviscid and irrotational fluid. Considering the effects of gravity, buoyancy, drag to the motion of bubble, the equations of motion (EOM) for bubble in inviscid and irrotational fluid near a free surface were established by introducing the potential-flow theory, energy equation and Hamilton principle. The displacement of the center of bubble, the radius-time histories and impulse periods of bubble were acquired by solving the EOM. The calculated results were compared with the experimental and numerical results. The compared results show that the former is consistent with the latter. The research has value to correlative theory research and engineering calculation.