In this study, the influence of the non-uniform surface of F- and O-functionalized Ti₂C on the anchoring behavior of lithium polysulfide (LiPS) is investigated using density functional theory. In order to consider the non-uniform surface, the substitutional, vacancy, and S-trapped sites of F- and O-functionalized Ti₂C are designed. The anchoring behavior is investigated considering the adsorption energy of LiPS, reactivity between Li atoms and the substrate, and the reduction state of the S atoms. On the F-substitutional site of the O-functionalized surface, it is confirmed that the suppressing mechanism changes from the neutralization of S atoms to the anchoring of LiPS. However, too strong of an interaction between Ti atoms exposed at the vacancy site and S atoms induces trapping of the S atom at the vacancies of both F- and O-functionalized surfaces. As a result of the trapping of the S atom, the use of active material decreases. In addition, the S-trapped site originated from the vacancy site does not affect the suppressing mechanism. In conclusion, to optimize the Ti₂C-based MXene as an anchoring material for Li-S batteries, the preparation process should be focused on eliminating the vacancy of functional groups.