  Topological quantum catalysts (TQCs), where metallic surface states from
nontrivial band topology serve as the mechanism to favor heterogeneous
catalysis processes, have been well demonstrated in three dimensional (3D)
examples but have been rarely discussed in 2D scale. Here, we develop a design
scheme to realize 2D TQCs with showing traversing nodal line at the Brillouin
zone boundary, large Fermi arc on the edge, and nearly zero Gibbs free energy
({\Delta}GH*) for hydrogen evolution reaction (HER). We demonstrate the 2D
Cu2C2N4 sheet is a such example. The material manifests an open nodal line
traversing the whole k-path S-Y. It shows a long Fermi arc that spans the
entire edge boundary, which is robust against spin-orbit coupling and the H
adsorption. As the result, the edge of Cu2C2N4 sheet is relatively active for
HER catalysis with possessing a {\Delta}GH* as low as 0.10 eV, which is
comparable with that of Pt and superior to other traditional catalysts and 3D
TQCs as well. Our work offers an effective route to develop high performance
HER catalysis without containing noble metals by utilizing 2D TQCs with
traversing nodal line.
