It is of practical significance to find organic metal-free catalyst materials. We propose a new graphene-like carbon nitride structure, which was able to meet these requirements well. Its primitive cell consists of eight carbon atoms and six nitrogen atoms. Hence, we called this structure g–C₈N₆. The stability of the structure was verified by phonon spectroscopy and molecular dynamics simulations. Then its electronic structure was calculated, and its band edge position was compared with the redox potential of water. We analyzed its optical properties and electron–hole recombination rate. After the above analysis, it is predicted that it is a suitable photocatalyst material. To improve its photocatalytic performance, two methods were proposed: applied tensile force and multilayer stacking. Our research is instructive for the photocatalytic application of this kind of materials.