Residual infrared absorption is a key problem affecting the laser emission efficiency of Ti:sapphire crystal. In this paper, the origin of residual infrared absorption of Ti:sapphire crystal is systematically studied by using the first principles method. According to the contact conditions of O octahedron in the crystal structure of Al2O3, four Ti3+-Ti3+ ion pair models and three Ti4+-Ti3+ ion pair models were defined and constructed. For what we believe is the first time, the near-infrared absorption spectra consistent with the experimental results were obtained in specific theoretical models. The electronic structures, absorption spectra, and charge distributions calculated show that the line-contact Ti3+-Ti3+ ion pair with antiferromagnetic coupling and the face-contact Ti4+-Ti3+ ion pair are two main contributors to the residual infrared absorption of Ti:sapphire, while some other ion pair models provide a basis to explain more complex residual infrared absorption.