In this study, an experimental investigation was conducted on the axial compression performance of ribbed H-section aluminum alloy members with initial curvature and torsion angle under varying boundary conditions, including one end hinged with the other rigidly connected, and both ends rigidly connected. Ultimate bearing capacity and failure modes were identified under real loads and subsequently compared with previous findings from our research group on members with hinged ends. To account for initial imperfections introduced during processing and transportation, 3D scanning technology was utilized to capture the precise geometrical dimensions, constructing an accurate numerical simulation model. The experimental results were corroborated with numerical simulations, leading to the proposal of an analytical method for members with initial curvature and torsion angle. Furthermore, extensive parametric analysis elucidated the impact of initial curvature, torsion angle, and slenderness ratio on the ultimate bearing capacity, culminating in the formulation of the stability factor and calculated length factor based on numerical outcomes. The study discovered significant variances in bearing capacity under different boundary conditions, with one-end hinged and one-section rigidly connected, and two-end rigidly connected conditions exhibiting 1.4 and 2.1 times the capacity of the hinged-at-both-ends scenario. Under different boundary conditions, the axial compression members were subjected to flexural-torsional buckling failure. Moreover, when the ultimate bearing capacity was reached, the lower flange of the member and the web near the lower flange appeared obvious buckling phenomenon. The numerical analysis aligned well with experimental data, validating the simulation method's reliability and revealing the stress distribution and evolution during member failure. These findings offer vital theoretical insights and technical support for engineering design and practical applications.