Two-dimensional Mo2C materials (1T and 2H phases) have emerged as promising electrocatalysts for the hydrogen evolution reaction (HER) due to their low cost, inherent metallicity, and high stability. Unfortunately, the catalytic activity of Mo2C is lower than that of Pt, and it needs to be substantially improved for practical applications. It is necessary and urgent to consider the effect of synergetic interactions among defects, functions, and strain on the HER activity. In this study, the geometric structures, electronic properties, and the HER activity of the Mo2C monolayer, with vacancy defects (i.e. Mo and C), oxygen functionalization, and strain, are studied by using first-principles calculations. According to our results, the combination of Mo vacancies, which can be obtained under C-rich conditions, and oxygen functionalization is the most effective way to improve the HER activity of 1T- and 2H-Mo2C. Considering the abundant active sites and optimal Gibbs free energy of hydrogen adsorption, the 1T phase we obtained shows excellent HER activity even at high H coverage and improves the utilization of active sites, for which the HER activity is comparable to that of Pt. This can be attributed to the fact that oxygen atoms gain more electrons from Mo2C, which weakens the strength of the O-H bond. Our work provides not only an opportunity to better understand the catalytic mechanism, but also a guide to achieving high HER activity of a Mo2C monolayer.