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Wide band gap group III-N materials are given due attention for the huge potential applications for fabricating novel opto-electronic devices. Group III nitride wide band gap semiconducting materials, in general, have a high melting point, high thermal conductivity and transparency to a large spectrum. These materials can be used for short-wavelength light emitting diodes, laser diodes and optical detectors and high electron mobility transistors 1. Group III nitride heterostructures have huge spontaneous and piezoelectric polarization. Boron nitride is found to be in the hexagonal phase with the zinc-blende structure and it is hard material 2. Boron nitride and Gallium nitride materials are considered to be the promising wide band gap candidates ranging from the ultraviolet to the visible regions of the spectrum. In the present work, the binding energy of a hydrogenic donor and the third order susceptibility of third order harmonic generation are discussed in a BxGa1-xN/BN quantum well. The barrier material is taken as GaN semiconductor whereas the Boron nitride material acts as inner well material. The energy eigen value and thereby the hydrogenic binding energy are obtained using variational technique within a single band effective mass approximation. The nonlinear optical property is investigated using density matrix method. The results can be applied for short wavelength optical devices.