The ceramic material Li₂ZrO₃ has superior thermo-physical and thermo-chemical properties and is highly compatible with other blanket materials used in nuclear reactors. Like LiAlO₂, it could be used in the form of an annular pellet in tritium-producing burnable absorber rods (TPBARs) to produce tritium(³H) upon thermal neutron irradiation of lithium isotope (⁶Li). The radiation damaged pellet crystal contains vacancies, defects of its constituent elements, and several other trapping sites which hinder the ³H diffusion process and releasing behavior. In this study, we investigate the diffusion mechanisms of ³H and O³H species in Li₂ZrO₃ ceramic pellet in order to understand the effects on diffusion barriers and diffusion coefficients due to the presence of interstitial and substitutional Li defects, hydroxide (O–³H) vacancy defect, and of the interactions of ³H with O-vacancies in the radiation damaged Li₂ZrO₃ crystal. We consider several possible diffusion pathways of interstitial and substitutional ³H and its species in a defective supercell and calculate the activation energy barrier profiles. We find that the smallest activation energy barrier is 0.3 eV and corresponding diffusion coefficient at 600 K is 1.93 × 10^–9 m²/s for ³H substitutional diffusion. The smallest ³H interstitial diffusion barrier and diffusion coefficient are found to be 0.34 eV and 3.25 × 10^–9 m²/s. By examining several channels for diffusion, our results show the most likely diffusion mechanism of ³H migration is occurring along the c-direction by exchange of ³H within and between different Li sites. Our calculated results reveal that the smallest energy barrier for O³H diffusion is 0.75 eV which is when O³H is diffusing to the O–Li vacancy pair and the corresponding diffusion coefficient is 6.31 × 10^–13 m²/s. In terms of ³H diffusion, the obtained results indicate that the performance of Li₂ZrO₃ could be better than γ-LiAlO₂, a widely used ceramic material in TPBAR for producing ³H.