Three types of graphyne, namely alpha-, beta-, and gamma-graphynes, have been doped with BN pair of different concentrations. The electronic band structure and optical properties of these doped graphynes are systematically investigated by the first-principles calculations. Band gap opening has been observed for BN pair-doped alpha- and beta-graphynes. Particularly, the BN pair-doped alpha-graphyne of different concentration is direct band gap semiconductor with tunable band gap. Band gap of BN pair-doped gamma-graphyne increases with the increase in doping concentration. Interestingly, an increase in doping concentration gives rise to a blue shift of the complex dielectric function epsilon(omega), reflectivity R(omega) and refractive index n(omega) under parallel polarization. As for BN pair-doped alpha-graphyne, the static dielectric constant, the maximum reflectivity coefficient and refractive index decrease monotonically with the increase in doping concentration under parallel polarization, whereas for perpendicular polarization the corresponding optical parameters are insensitive to the doping concentration. Furthermore, the first dominant peak of the imaginary part of dielectric function is extended from the infrared region to the ultraviolet region when increasing the doping concentration. With regard to BN pair-doped beta- and gamma-graphynes, the optical properties exhibit similar features as that of BN pair-doped alpha-graphyne.