Although the Li diffusion in sin- gle crystalline γ-LiAlO2 was stud- ied with temperature-dependent Li- 7 NMR spectroscopy and conductivity measurements recently, the exact diffu- sion pathways are not clearly identified yet. Therefore the present study aims at elucidating the diffusion pathways in γ-LiAlO2 theoretically from first principles. Competing pathways for Li diffusion are investigated using the climbing-image Nudged-Elastic-Band approach with periodic quantum- chemical DFT method. Li can migrate between two regular LiO4 tetrahedral sites via Li point defect (VLi ) and via a Li Frenkel defect (VLi+Lii ). On the basis of calculated activation energies for Li diffusion pathways, it is con- cluded that Li conductivity is strongly dependent on the distribution of Li vacancies and interstitial Li in the lat- tice. For Frenkel defects where Lii is far away from the migrating Li atom, the calculated activation energies for jumps to nearest-neighbor vacant sites agree with experimental values.