Native defect-induced photoluminescence around 400nm (blue luminescence - BL) was studied in hBN materials with different size and various origins. The following spectral characterizations were used: spectra of luminescence and its excitation, luminescence dependence on temperature, luminescence kinetics, optically stimulated luminescence and infrared absorption. It was found, that the BL is characteristic for all these materials, which were studied. The BL forms a wide, asymmetric and phonon-assisted emission band at 380nm. This luminescence can be excited either through the exciton processes, or with light from two defect-induced excitation bands at 340nm and 265nm. It was found that the BL is caused by two luminescence mechanisms. One of them is intra-center luminescence mechanism (340nm excitation), but the other one is recombination mechanism (265nm excitation). It was considered that the most probable candidates for the defects, which cause the BL in hBN can be related to the nitrogen vacancy type-centers. It was certainly confirmed, that presence of oxygen gas is partly quenching the BL intensity, thus ranking the hBN material among the materials prospective for development of oxygen gas optical sensors. •Defect-induced luminescence at 380nm is observed for hBN powders.•A phonon-assisted structure is characteristic for 380nm luminescence.•The defect-related excitation of 380nm luminescence is at 340nm and 265nm.•The 380nm luminescence is caused by a recombination or an intra-center mechanism.•The 380nm luminescence is sensitive to oxygen gas environment.