In this paper, the laser welding process of 6082-T6 and 6063-T6 dissimilar aluminum alloys with a thickness of 2.5 mm was numerically simulated by using a rotary surface Gauss heat source and the flow state of the weld pool was analyzed. The microstructure and mechanical properties of the welded joint (WJ) with a laser power of 1.75 kW were also studied. The results show that the recoil pressure in the molten pool tends to be stable with the increase in welding power, and the surface tension was the main driving force affecting the liquid metal flow in the molten pool. Under the action of 1.75 kW of laser power, the macromorphology of the weld was complete, continuous, and clear. The weld metal zone (WMZ) near both sides of the fusion line (FL) was columnar in microstructure, and the center of the WMZ was dominated by equiaxed crystals. The average microhardness of WMZ was 73.46 HV, which was lower than the base material zone (BM) and heat-affected zone (HAZ). The fracture region of the tensile specimen was located in HAZ on the 6063-T6 side of WJ, showing ductile fracture characteristics with a tensile strength of 180.8 MPa and elongation of 4.04%.