Three novel hexagonal Si-C-N structures, namely SiC3N3, SiC7N6, and SiC13N14, were constructed on the basis of the α-Si3N4 crystal structure. The stability of the three structures is demonstrated by analyzing their elastic constants and phonon dispersion spectra and by calculating their formation energies. The calculated band structures and partial densities of states suggest that the SiC3N3 and SiC7N6 structures possess hole conductivity. The electron orbital analyses indicate that the SiC3N3 and SiC7N6 crystals possess three-dimensional and one-dimensional conductivity, respectively. SiC13N14 is a semiconductor with a wide bandgap of 4.39 eV. Based on two different hardness models and indentation shear stress calculations, the Vickers hardness values of SiC3N3, SiC7N6, and SiC13N14 are estimated to be 28.04/28.45/16.18 GPa, 31.17/34.19/20.24 GPa, and 40.60/41.59/36.40 GPa. This result indicates that SiC3N3 and SiC7N6 are conductive hard materials while SiC13N14 is a quasi superhard material.