The electronic energy bands of a series of β phases of carbon nitride, silicon nitride and germanium nitride have been calculated using a first-principle linear combination of muffin-tin orbital method with the atomic-sphere approximation(LMTO-ASA). The band gaps obtained for the three compounds are 4. 1751,5. 1788 and 4. 0279 eV, respectively. For β-C3N4 ,the nitrogen 2p orbitals plays an important role in the top of valence band(VB) due to its non-bonding. For -β-Si3N4,the silicon 3d orbitals plays an important role both in the VB and in the conduction band(CB). Its band gap is indirect which is in agreement with other calculated results. For β-Ge3N4,the germanium 3d orbitals preserve the characteristics of atomic orbitals and give very little contributions to other VBs and CB. Its 4d empty orbitals play a role analogue to 3d of Si of β-Si3N4. This is the frist theoretical study reported on the electronic structure of β-Ge3N4.