This paper proposes an integral hydrobulge forming (IHBF) method using a triangular patch polyhedron as the closed preform shell. When triangular flat parts are welded along the edges in sequence, triangular patch polyhedra are naturally formed. From the radius of the spherical pressure vessel, a design formula was derived to calculate the side lengths of the triangular flat plate parts. The water pressure, water volume, average strain of molding, and amount of springback after molding, which are necessary for implementing the IHBF for practical use, were also formulated. To verify the forming performance of the spherical pressure vessel using IHBF method, the finite element method was carried out, and a stainless-steel spherical pressure vessel with a thickness of 1.0 mm and a diameter of approximately 500 mm was fabricated using the proposed IHBF method. As a result, the measured shape error expressed as roundness to diameter ratio was 0.52%, and the calculated average plastic strain was 0.02, which was approximately 1/19 times of the forming limit strain of the material. The amount of springback after forming by calculation was approximately 0.7 mm, indicating that the amount of water required for IHBF was 5.90% of the volume of the spherical pressure vessel, while the required water pressure was no bigger than 2.3 MPa. The process directly utilizes triangular flat plate parts, eliminating the need for molds to process closed preform shells resulting in a low average plastic strain during forming, thereby improving the quality of the formed spherical pressure vessels.