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Cosmological features of Barrow Holographic Dark Energy (BHDE), a recent generalization of original Holographic dark energy with a richer structure, are studied in the context of DGP brane, RS II brane-world, and the cyclic universe. It is found that a flat FRW scenario with pressure less dust and a dark energy component described as BHDE can accommodate late time acceleration with Hubble horizon considered as infrared cut off even in the absence of interaction between the dark sectors. Statefinder diagnostic reveals that these model resemble $ΛCDM$ cosmology in future. It is found that BHDE parameter $Δ$, despite its theoretically constrained range of values, is significant in describing the evolution of the universe, however, a classically stable cosmological model cannot be obtained in the RS-II and DGP brane. Viability of the models is also probed with observed Hubble data.