With the novel dual heat source model for pulsed laser-gas tungsten arc (GTA) hybrid welding by COMSOL Multiphysics, the temperature distribution was analyzed at several selected points along the weld line. The influences of laser pulse parameters and electric arc current on the welding pool morphology were investigated. The results show that the influence of different process parameters on the depth of molten pool ranked in order is as follows: laser excitation current>arc current>laser pulse width>laser pulse frequency. The influence of different process parameters on the width of molten pool ranked in order is as follows: arc current>laser pulse width or laser excitation current>laser pulse frequency. A database of molten weld pool characteristics for laser-induced arc welding of magnesium alloy was established by classifying the composite heat source parameters and used to realize the precise control of the molten pool shape. The precise control of the actual welding molten pool of a T-shaped weld is achieved with accuracy of 95.1%.