The invention discloses a rubber forming method and a rubber forming mould of a high-curvature high-flanging sheet metal part. The rubber forming mould comprises an accommodating box, a forming die, a pressing plate, a supporting plate and rubber pads, wherein the non-working surface on the inner side of the forming die is connected to the inner wall of one side of the accommodating box; a moulding cavity is formed between the working surface on the outer side of the forming die and the inner wall of the accommodating box; the outlines of the pressing plate and the supporting plate are smaller than the outline of the moulding cavity; the inner sides of the pressing plate and the supporting plate are matched with the working surface on the outer side of the forming die. The rubber forming method comprises the following steps: placing the accommodating box on a workbench of a hydraulic machine, placing a plurality of rubber pads with equal height inside the moulding cavity, and placing the supporting plate on the upper surfaces of the rubber pads so as to make the surface height of the supporting plate consistent with the height of the forming die; overlapping the pressing plate and the supporting plate, and clamping a flanging area of an unfolded blank; downwardly pressing the pressing plate by using hydraulic forming equipment, fitting the flanging area of the unfolded blank with the working mould surface of the forming die, and forming.