The full potential linearized augmented plane wave method with the generalized gradient approximation has been used to understand the electronic and optical properties of agraphyne- likeBN(a-BNyne) sheet. The total and partial density of states, electronic structure and optical constants for different light polarizations are obtained. The optical properties of a- BNyne are found to be strongly anisotropic. For electric field parallel to the a-BNyne sheet, strong optical adsorption and reflectivity are observed in the low-energy region, whiles for the electric field perpendicular to the a-BNyne sheet, the adsorption and reflectivity in the lowenergy region are very weak. Also, the results of optical response property calculations show that a-BNyne sheet has broad spectral photoresponse. All of these properties indicate that a- BNyne is a new two-dimensional candidate for use in optoelectronic devices.