Curved prisms can serve as core components of dispersive spectroscopy and converge light paths, making them widely used in spectral imaging technology. Their positional stability, surface shape errors, and temperature stability in optical systems directly affect the performance of spectral imaging systems. On the basis of the analysis of design indicators and optimization of the support structure for curved prisms, a multipoint flexible adhesive support structure (MPPASS) of large rectangular curved prisms for space-based application is proposed. The novelty of the MPPASS lies in its ability to achieve micro-stress and high stability support for large-aperture rectangular optical elements through the bonding of peripheral small points and the introduction of flexible bonding rings. The design principles of the adhesive support structure were deeply studied, and on this basis, the engineering design, finite element analysis, adhesive testing, and mechanical testing of large curved prisms were completed. The designed curved prism assembly has a maximum deformation displacement of 0.0085 mm and a maximum tilt angle of 0.65” under gravity loading, a first-order frequency of 1003.5 Hz, and a maximum acceleration amplification factor of 3.12 in the X, Y, and Z directions. The root mean square (RMS) variation value of the mirror shape errors for the curved prism assembly was 5.26 nm under a uniform temperature load of 20 ± 1 °C, and the RMS value of the mirror shape errors was 0.019 λ after mechanical testing. The installation surface flatness of 0.02 mm did not significantly affect its mirror shape errors. The experimental results verified the rationality of the design, temperature stability, and mechanical stability of the MPPASS.