We report on the demonstration of MoS2/GaN UV-visible photodetectors with high spectral responsivity both in UV and in visible regions as well as the observation of MoS2 band-edge in spectral responsivity. Multi-layer MoS2 flakes of thickness ~ 200 nm were exfoliated on epitaxial GaN-on-sapphire, followed by fabrication of detectors in a lateral Metal-Semiconductor-Metal (MSM) geometry with Ni/Au contacts which were insulated from the GaN layer underneath by Al2O3 dielectric. Devices exhibited distinct steps in spectral responsivity at 365 nm and at ~ 685 nm with a corresponding photo-to-dark current ratio of ~4000 and ~ 100 respectively. Responsivity of 0.1 A/W (at 10 V) was measured at 365 nm corresponding to GaN band edge, while the second band edge at ~ 685 nm is characterized by a spectral responsivity (SR) of ~ 33 A/W when accounted for the flake size, corresponding to the direct band gap at K point of multi-layer MoS2.