Disclosed are an apparatus and a method for deep drawing of large-sized thin-wall curved surface parts with servo reverse bulging, which pertain to the technical field of drawing of a thin-wall curved surface part. The apparatus includes a forming die, a jacking unit, and a power unit, wherein the forming die includes an upper die, a lower die, and a blank holder. The upper die and the blank holder are connected to a press machine, the blank holder is disposed above the lower die, and a blank to be drawn is placed between the lower die and the blank holder; the jacking unit is disposed inside the lower die and adapted to move along a moving direction of the upper die, enabling the blank to be drawn to deform by with reverse bulging. The method can inhibit defects of wrinkling and cracking in drawing processes effectively.