Manned pressure shells subjected to deep-sea pressure are designed with a spherical shell structure because they are subjected to perfectly symmetrical pressures. A spherical pressure shell has excellent mechanical properties against deep-sea pressure; therefore, it has the advantage of relatively good buckling properties. However, there are high demands on the processing accuracy of spherical pressure shells, such as thickness distribution and roundness. Even when a small asymmetrical element is present, the buckling characteristics under deep-sea pressure are significantly reduced. In this paper, we propose a new type of spherical pressure shell composed of multiple triangular-plate parts and an integral hydrobulging forming (IHBF) method to process it. Specifically, multiple triangular metal plate parts were prepared and welded along the right side to form a preformed box. A spherical pressure shell was plastically formed by applying water pressure to the interior of the preformed box, causing it to expand outward. For verification, an actual molding experiment was conducted using a spherical pressure shell with a design radius of 250 mm as the research object. The measurement of the outer surface shape of the formed spherical pressure shell showed that the radius value of the spherical pressure shell was 246.52 mm, the error from the design radius was 1.39%, the roundness of the spherical surface was 3.81 mm, and the maximum reduction rate of the plate thickness was 3.2%. Therefore, the processing quality of the proposed IHBF method was confirmed to be high. Buckling analysis was performed by applying a uniformly distributed external pressure to simulate the deep-sea pressure. Compared with the conventional spherical shell structure, the crushing/buckling load of the spherical pressure shell processed by the IHBF method proposed herein is affected by work hardening owing to plastic forming, local defects, and welding line. The effect of the size is relatively small.