β-C_3N_4 compound is a new hard material predicted by Liu and Cohen with theoretical calculation and so far it has not been found out in nature. In was assumed that the β-C_3N_4 compound would adopt the known crystal structure of β-Si_3N_4, which constructed a network of CN_4 tetrahedra linked at the corners by threefold coordinate N atoms. Thus, the atomic coordination of β-C_3N_4 is sp~3 hybrids on the C atoms and sp~2 hybrids on the N atoms. Based on the theoretical analysis and modeling calculation, it was β-C_3N_4 compound is a new hard material predicted by Liu and Cohen with theoretical calculation and so far it has not been found out in nature. In was assumed that the β-C_3N_4 compound would adopt the known crystal structure of β-Si_3N_4, which constructed a network of CN 4 tetrahedra linked at the corners by three fold coordinates N atoms. Thus, the atomic coordination of β-C_3N_4 is sp ~ 3 hybrids on the C atoms and sp ~ 2 hybrids on the N atoms. Based on the theoretical analysis and modeling calculation, it was