[en] Highlights: • Li atom is adsorbed on MoO₂ and WO₂ sheets rather stronger than all other MX₂ systems investigated. • The energy barrier for diffusion of single Li on MX₂ varies between 0.15 eV and 0.28 eV which are lower or comparable to that of graphene or silicene. • The adsorption energy values do not remarkably change with increasing number of adsorbed Li atoms. - Abstract: It is important to improve the high-efficient anode materials for Li batteries, which require the large capacity, high stability and mobility. In this work, we present the adsorption and diffusion properties of lithium atom on MX₂ (M = Mo, W; X = O, S, Se, Te) transition metal dichalcogenide structures using first principles calculations within density functional theory. All the MX₂ systems considered are semiconductor in bare state with band gaps between 0.93 eV (MoO₂) and 1.79 eV (WS₂). They turn into metal upon single Li adsorption. Li atom is adsorbed on MoO₂ and WO₂ rather stronger than other systems. The energy barrier for diffusion of single Li on MX₂ varies between 0.15 eV and 0.28 eV which are lower or comparable to that of graphene or silicene. Two Li atoms are preferably adsorbed on MX₂ monolayer symmetrically at opposite sides with high adsorption energy. The increasing number of Li atoms does not remarkably affect the adsorption energy per Li atom. This can be attributed to that Li atoms do not accumulate on certain regions of the surface. The systems under investigation provide insights into exploring electronic properties which are rather adequate for possible applications in Li-ion batteries.