Currently, finding the non-precious metal catalyst for hydrogen evolution reaction (HER) is significant and urgent. By performing the first-principles calculations, we studied the structural and electronic properties, as well as the catalytic activity of MXenes Mn+1CnO2 (n=1, 2; M=Sc, Ti, V, Cr, Mn, Zr, Nb, Mo, Hf, Ta and W) toward HER. These 22 MXenes are metallic except for Sc2CO2, Ti2CO2, Mn2CO2, Zr2CO2 and Hf2CO2 which are semiconducting. By calculating the Gibbs free energy change (G(H)) for H adsorption which is the simple but effective descriptor for HER catalytic activity, and analyzing the electrical conductivity, we find that Nb2CO2, W2CO2, Zr3C2O2 and W3C2O2 are catalytic active for HER at low H coverage. Particularly, Nb2CO2 and Zr3C2O2 maintain to be active for catalyzing HER under tensile strain less than 5%. And Nb3C2O2 shows enhanced catalytic activity for HER under 3-5% tensile strain. Additionally, the differential G(H) and average G(H) were used to evaluate the HER catalytic activity at high H coverage (1/8-6/8). Our calculations show that Nb2CO2 is active for HER at H coverage less than 3/8. Plus, V2CO2, Ti3C2O2 and Cr3C2O2 demonstrate the catalytic activity for HER at high H coverage.