The metal diboride family has been systematically studied in recent years due to the discovery of superconductivity for magnesium diboride MgB 2 at 39 K. TiB 2 is the most stable of several titaniumboron compounds, due to its high hardness, extreme melting point and chemical inertness. TiB 2 is a candidate for a number of applications; it is used for wear parts and in composites with other materials. In combination with other primarily oxide ceramics, TiB 2 is used to constitute composite materials in which the presence of the material serves to increase the strength and fracture toughness of the matrix. In our paper, the electronic structure of AlB 2 -type transition metal diboride of TiB 2 , NbB 2 and their ternary alloy Ti 0.5 Nb 0.5 B 2 have been calculated by using the full potential linearized augmented plane wave method with local orbitals (APW + lo). We included the exchange correlation potential by using both the generalized gradient approximation (GGA) and the local density approximation (LDA), respectively, as embodied in the Wien2 K in full relativistic version. The electronic structure is discussed and the rigid band model is shown to provide a fairly good description. The Ti-3d and Nb-4d electron are treated as valence electrons. We explained in some detail the bonding nature of our compounds. The existence of the pseudogap in the total densities is found to be a common feature of these compounds, but we found that the pseudogap at Fermi-levels of TiB 2 is the competing effect of Ti-3d resonance and strong hybridization between Ti-3d and B-2p states. The variation of the chemical stabilities of these diborides is analysed. The results are compared with other theoretical and experimental work.