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Holey graphyne (HGY) is a recently synthesized two-dimensional semiconducting allotrope of carbon composed of a regular pattern of six and eight-vertex carbon rings. In this study, based on first-principles density functional theory and molecular dynamics simulations, we predict a similar stable porous boron nitride holey graphyne-like structure that we call BN-holey-graphyne (BN-HGY). The dynamical and thermal stability of the structure at room temperature is confirmed by performing calculations of the phonon dispersion relations, and also ab-initio molecular dynamics simulations. BN-HGY structure has a wide direct bandgap of 5.18 eV, which can be controllably tuned by substituting carbon, aluminum, silicon, and phosphorus atom in place of sp and sp$^2$ hybridized boron and nitrogen atoms of BN-HGY. We have also calculated the optical properties of the HGY and BN-HGY structures for the first time and found that the optical absorption spectra of these structures span full visible and a wide range of ultraviolet regions. We have found that the Gibbs free energy of the BN-HGY structure for the hydrogen adsorption process is very close to zero (-0.04 eV) and, therefore, the BN-HGY structure can be utilized as a potential catalyst for HER. Therefore, we propose that the boron nitride analog of holey graphyne can be synthesized and that it has a wide range of applications in nanoelectronics, optoelectronics, spintronics, ultraviolet laser, and solar cell devices.