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[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.