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In this paper, a N-rich B–N polymorph named as B₂₀N₂₄ is proposed through first-principles calculations. The stability of the B₂₀N₂₄ polymorph at ambient conditions is confirmed using the phonon dispersion spectra and the Born stability criteria. Electronic properties calculations show that B₂₀N₂₄ exhibits a semiconducting feature, with a 0.87 eV direct band gap derived from HSE06 functions, which is much lower than many other B–N polymorphs. Specifically, owing to its cage-like framework, B₂₀N₂₄ may be used in hydrogen storage at a capacity of ~6.8 wt.%. The B₂₀N₂₄ polymorph enriches the B–N system theoretically, and this polymorph is promising for use in electronic devices and hydrogen storage.