The two-dimensional electrochemical Y2C’s low work function and strong charge transfer qualities limit its applicability in catalysis due to its poor catalytic activity. In this paper, based on density functional theory calculations, we use two techniques to increase the HER catalytic activity of the Y2C monolayer: substitution doping (XC) and adsorption doping (XT) of non-metal (X = N, P, O, S, and F). The results showed that the absolute values of hydrogen free energies (ΔGH*) of the substitutional dopants of PC, SC and adsorptive dopants of NT, OT, ST, and PT had increased catalytic activity compared with those of the pristine Y2C monolayer (−0.673 eV). It was highlighted that the adsorption doping of PT can further reduce the adsorption free energy of the pristine Y2C monolayer to −0.19 eV, which is close to the optimal zero value, and the binding energy of the hydrogen atoms on the Y2C surface significantly increased from −0.913 to −0.438 eV, which is more favorable for the desorption of hydrogen atoms. These results demonstrate that the doping of non-metals activates the adsorption of hydrogen atoms on monolayer Y2C and provides a feasible method for hydrogen generation.