We have used the ab-initio SIESTA code within the framework of DFT, LDA methodrnto calculate the structural and electronic properties of BexZn1-xSe alloy for differentrncompositions x = 0.0, 0.33, 0.66, and 1.0. The system is modelled in various possiblernconfigurations using a large 54-atom supercell. It is noteworthy to mention that therndetermination of structural and electronic properties of a BexZn1-xSe ternary alloy at xrn= 0.33 and 0.66 have not been reported earlier to the best of our knowledge. Wernanalyze composition effect on lattice constants, bulk modulus, pressure derivative,rnbandgap, and density of states. Deviations of the lattice constant from Vegardâ€™s lawrnand the bulk modulus from linear concentration dependence are observed. It wasrndeduced that increasing the Be composition in the alloy increases the hardness of thernmaterials. In addition, the calculated band structures showed that the bandgaprnundergoes a direct-to-indirect transition at the composition of 0.84. The bandgap isrnfound to vary non-linearly with Be composition. Using the approach of Bernard andrnZunger, the microscopic origins of bandgap bowing is also explained. It is concludedrnthat the energy bandgap bowing is primarily due to volume deformation effect.rnFurthermore, the structural phase transformations of ZnSe under high pressure arernalso studied by similar method. It is found that ZnSe undergoes a first-order phaserntransition from the zinc blende structure to the rock salt structure at approximatelyrn13.75 GPa. The ground state properties of the phases of ZnSe are also calculated. Ourrnresults are in good agreements with experimental observations.