Formamidinium lead halide perovskite FAPbI3 (FA = HC(NH2)2+) has drawn wide attention as efficient photoelectronic conversion material. First-principles calcualtions were performed by using the Vienna ab initio simulation package (VASP) based on density functional theory. The structure configuration, electronic property, absorption spectrum, and bonding energy were analyzed to evaluate the effect of crystal deformation on photoelectronic properties of FAPbI3 perovskite. Results showed that the crystal deformation from trigonal to hexagonal crystal would distort the PbI3 framework, change the covalent/ionic Pb–I bonds, and eventually alter the semiconductor bandgaps. The trigonal and hexagonal FAPbI3 perovskites are both direct-bandgap semiconductors. The direct-bandgap nature of trigonal crystal locates at Z (0, 0, 0.5) symmetry point with the ideal bandgap of ~1.50 eV; the direct-bandgap nature of hexagonal crystal locates at Γ (0, 0, 0) symmetry point with the wide bandgap of ~2.50 eV. For the both crystals, the main contributions to VBM are I 5p orbitals with a little overlapping of Pb 6s orbitals. For the trigonal FAPbI3, the main components of CBM are Pb 6p orbitals. Whereas for the hexagonal FAPbI3, the main components of CBM are Pb 6p with some admixture of I 5p orbitals. The FA cations do not directly participate into the electron transition process, just acting as charge donors to supply PbI3 framework with more than 0.7 e. There exists both covalent and ionic interactions between Pb and I ions. Compared with the hexagonal crystal, the trigonal FAPbI3 exhibits dramatic red shifted absorption spectrum. The trigonal FAPbI3 exhibited a better absorption efficiency than hexagonal FAPbI3 and tetragonal MAPbI3 (MA = CH3NH3+) perovskites. Bonding energy analyses showed that the hexagonal FAPbI3 was more stable than the trigonal crystal, and interaction between FA and PbI3 framework was stronger than that between MA and PbI3 framework. Our results could provide theoretical guidence for the experimental design and synthesis of FAPbI3 perovskite solar cells.