We present first principles calculations of the structural and electronic properties of zinc blende BN, InN and their ternary alloy B x In 1−x N for concentrations x = 0.25, 0.5, 0.75. The computational method used is based on the full potential linearized augmented plane wave. The exchange and correlation energy is described in the local density approximation and generalized gradient approximation. We have studied the structural and electronic properties. First, the lattice constants a 0 , bulk modulus B, pressure derivative B for zinc blende BN, InN, and B x In 1−x N solid solutions were carried out. Thereafter, the band gap energies and the densities of states of binary compounds and the ternary alloy B x In 1−x N were investigated. Results obtained and compared with available experimental and theoretical values show a reasonable agreement.