The invention relates to a novel short circuit transition welding system of coupling arcs and a control method thereof, and belongs to the field of a welding method and equipment and automation. The system adopts a digital chip DSP (Digital Signal Processing) control means to complete the control of the short circuit transition welding process of hybrid welding of direct current MAG and TIG. In the welding process, two arcs are respectively controlled by independent power supplies, the power supplies form communication connection, main arcs are formed between MAG welding wires and base metal, and a molten drop transition mode of short circuit transition is adopted. Auxiliary arcs are formed between TIG electrode and the welding wires. Based on the total output current 150 A-250 A of MAG and TIG, the control method controls the output current I1 of the TIG power supply in an arcing phase to melt more welding wires to fill weld joints, and I1 is at least 80 A and at most 200 A; the control method controls the output current I2 of the TIG power supply in a short circuit phase to maintain the stability of arcs, and the I2 is at least 20 A and is at most 80 A. According to the system and the method, the precise control problem of energy during short circuit transition welding is solved, the independent adjustment function of the heat input of the base metal and the amount of deposited metal is realized, and the heat input of the base metal can be controlled and adjusted.