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Exploring novel three-dimensional (3D) perovskite photovoltaic materials with high performance and optimal bandgap is an attractive strategy for expanding the perovskite family and replacing the currently widely studied, unstable CH3NH3PbI3perovskite materials. To achieve stable, 3D perovskite materials with excellent performance, five small organic cations (AM1, AM2, FM1, FM2, and DM) were introduced into the A-site of ABX3perovskite. The geometric structure, thermodynamic stability, electronic properties, and carrier transport properties of these materials were investigated using first-principles calculations. Additionally, the bandgap tunability and structural stability of these materials under different pressures were studied. The research results indicate that the replacement of different organic cations can produce highly stable perovskite phases with suitable direct bandgaps and smaller effective electron and hole masses. Theoretical calculations demonstrate that FMPbI3-1, FMPbI3-2, and DMPbI33D organic–inorganic hybrid perovskites exhibit excellent bandgap adjustability, and the optimal photovoltaic bandgap can be achieved through pressure tuning. Combined with large light absorption, small exciton binding energy, high carrier mobility, and high power conversion efficiency, these materials are expected to achieve unique photovoltaic device performance and applications.