We have grown various epitaxial GaN nanostructures on sapphire (11–20) substrates by tuning the buffer layer growth conditions in laser molecular beam epitaxy (LMBE) process. The pre-nitridation and buffer layer GaN growth at low temperature (LT) on sapphire (11–20) critically affect the surface morphology and structural properties. Granular GaN thin film (~ 160 nm) was grown on pre-nitridated sapphire whereas nano-column (NC)-GaN was obtained on LT-GaN buffer layer on bare sapphire having a height of ~ 370 nm at the growth temperature of 700 °C. Nano-porous (NP)-GaN was obtained with pore sizes in the range of 70 ~ 110 nm having vertical height of ~ 560 nm under similar growth conditions on LT-GaN buffered pre-nitridated sapphire. In-situ reflection high energy electron diffraction, high-resolution x-ray diffraction and Raman spectroscopy measurements indicated the epitaxial growth of c-axis oriented, wurtzite crystalline GaN nanostructures on sapphire (11–20) substrate with nearly negligible biaxial stress (0.03–0.23 GPa). Further, metal-semiconductor-metal (MSM) ultra-violet (UV) photodetectors were fabricated on epitaxial GaN nanostructures. The photo responsivity studies revealed that the NP-GaN MSM device has a photoresponse of ~ 358 mA/W at an applied bias of 1V. The photo-responsivity of NP-GaN MSM device is higher than that of GaN film (~ 36 mA/W) and NC-GaN (~7 mA/W) which revealed the importance of shape and size of GaN nanostructures on the responsivity of UV-photodetector devices. These results demonstrate the capability of LMBE technique to grow different GaN nanostructures on sapphire (11–20) substrate by tuning buffer layer conditions for their application as UV-photodetectors.