First-principles calculations with supercell (SC) method and virtual crystal approximation (VCA) method were preformed to study the formation energy, mixing energy, lattice constant, volume, elastic constants, melting points, elastic modulus, vickers hardness, fracture toughness and density of states of (Ti/Zr)1-x(Ta/Nb)xB2 (0≤x≤1) solid solutions. The formation energy results show that the structural stability of the diboride solid solution of (Ti/Zr)1-x(Ta/Nb)xB2 decreases with the increase of the concentration of doped atoms. The volume of Ti1-x(Ta/Nb)xB2 increases with the increase of the concentration of doped atoms, because the atomic radii of Ta and Nb are larger than Ti. While the volume of Zr1-x(Ta/Nb)xB2 becomes smaller, since the atomic radius of Ta and Nb is smaller than that of Zr. Moreover, the diboride solid solution of (Ti/Zr)1-x(Ta/Nb)xB2 are mechanically stable and brittle materials. In particular, Ta and Nb dopants can significantly improve the brittleness, bulk modulus and fracture toughness of the solid solution (Ti/Zr)1-x(Ta/Nb)xB2, and reduce their vickers hardness.