We present structural and electronic properties of the cubic structure for different concentrations x of ternary alloy $B_x Ga_{1-x}N$. The computational method is based on the full-potential linearised augmented plane wave method (FP-LAPW). The exchange and correlation energy is described in the local density approximation (LDA) and generalized gradient approximation (GGA). We have investigated the effect of composition on the ground state properties, lattice parameters, bulk modulus, pressure derivative and band gap of the zinc blend BN and GaN. The results obtained are in a good agreement with experimental and theoretical values concerning the variation of the gaps and crossover direct, indirect band gap and the bowing parameter. A reasonable agreement is found from the comparison of our results with other theoretical calculations.