Abstract: The transient thermo-flow-electromagnetic dynamic numerical model was proposed for the simulation of deep-penetration laser beam welding of 6 mm thick 5056 aluminum alloy under an external static magnetic field. The transient temperature, velocity and electromagnetic fields were calculated and the modeling of Peclet number within the welding pool was conducted. The influence of varying magnetic flux densities on molten flow and thermal transfer behavior was analyzed. The results shown that, significant Hartmann effect could be induced in the weld pool with static magnetic field aligned, resulting in Marangoni convection compression, melt flow deceleration and intensity reduction of thermal convection. Accordingly, the weld pool length contracted along the welding direction, and the solid-liquid interface became less curved. Meanwhile, the thermal hysteresis effect occurred at weld pool surface and inside. The local molten metal was heated and the temperature gradient was increased, leading to the increase of thermal diffusion rate and local extension of weld pool dimensions. The variations of seam profile in magnetically supported laser beam welding attributed to the synthetic actions of Hartmann effect and thermal hysteresis.