The MXenes, which are two-dimensional form of MAX phases, have been introduced as a potential candidate for hydrogen evolution reaction (HER) catalyst due to their high surface area and thermostability. Recent studies of MXenes as an HER catalyst have focused on interaction between hydrogen and the uniformly functionalized surface. However, synthesizing MXenes with uniformly functionalized surface is still remained as a main challenge in this field, which induces gap between experimental and theoretical results. In this study, to evaluate the activity of the HER, the adsorption properties of a hydrogen atom on the non-uniformly functionalized surfaces of Ti2C-based MXene were investigated using density functional theory (DFT). On the surface where fluorine and oxygen functional groups coexist, a hydrogen atom was turned out to be adsorbed on the top of oxygen functional group with slightly larger adsorption energy than the case on the uniformly oxygen functionalized surface. At the vicinity of oxygen vacancy, compared with adsorption energy of a hydrogen atom on the uniformly oxygen functionalized surface, much larger adsorption energy was obtained when a hydrogen atom interacted with the exposed transition metal while slightly smaller adsorption energy for the on top site of nearest oxygen from vacancy. The change of adsorption energy of a hydrogen atom affects Gibbs free energy difference of hydrogen, well-established criterion in HER research. The HER activity was evaluated via calculation of Gibbs free energy difference of hydrogen, which was derived from ab-initio thermodynamics. Through these results, it could be inferred that non-uniformly functionalized surface condition influenced the HER activity of Ti2C-based MXenes. Therefore, this theoretical study will provide further insight into the design of MXenes as a catalyst for HER.