The electronic and optical properties of α-graphyne/α-BNyne bilayer, without strain and under strain, are investigated from first-principles calculations. Monolayer α-graphyne has zero band gap and its electronic structure consists of Dirac cone. The zero band gap of α-graphyne is a major impediment for its applications as a semiconductor. The results reveal that an energy gap of 39 meV can be opened for the strain-free α-graphyne/α-BNyne bilayer. The created band gap increases by applying the in-plane biaxial strain and decreasing the interlayer distance. Applying the out-of-plane vertical strain leads to the transforming tendency from linear dispersion near the Fermi energy to parabolic-like dispersion. The linear dispersion of the bands and the position of the Dirac point do not change with the biaxial tensile strain. The peak positions of ε2(ω) spectrum for α-graphyne/α-BNyne bilayer shift to lower energies by applying the biaxial tensile strain, while its peak positions are not significantly shifted by the out-of-plane vertical strain.