Indium oxide with its wide gap is a multifunctional semiconductor material, which has gained application in many areas. Indium oxide films show high electrical property and high transparency, which have been applied in OLED display, flat-panel display, thin film solar cells, etc. However, the mechanisms of both high electrical and high transparent properties are still not clear up to now. So in this paper, the electronic structures of the In2O3 crystals are studied by GGA, GGA+U, HSE06 and G0W0 corrections. The mechanisms of optical transition and formation of transparent electrode in In2O3 crystals are studied using Hedin's G0W0 approximation and the Bethe-Salpeter equation. The complex refractive index, complex dielectric function and optical absorption spectrum of the In2O3 crystal have been obtained, which are in good agreement with experimental results. By analyzing the quasi-particle band structures, optical transition matrix and optical absorption spectrum, the mechanisms of optical transition and formation of transparent electrode in In2O3 can be interpreted. BSE (Bethe-Salpeter equation) calculation results show that the transition from 8 to 1 is permitted, however, the transition probability is far less than that from 10 to 1. This is because, for 8 to 1 transition, there are three even symmetry bands and two odd symmetry bands, in which only the transition from two odd symmetry bands to the conduction band is permitted. Other causes for this phenomenon are that in the In2O3 primitive cell there exist some overlapping bands, which result in the false transition. Therefore, this work argues that in the In2O3 crystals optical band gap is 4.167 eV, which corresponds to the direct transition from 10 to 1. This result will help understand the mechanisms of optical transition and the transparent electrode in In2O3.