We report the fabrication and optical and electrical characterization of photodetectors for the UV spectral range based on single p–n junction nanowires with a transparent contact of a new type. The contact is based on CVD-grown (chemical-vapor deposition) graphene. The active region of the nitride nanowires contains a set of 30 radial In_0.18Ga_0.82N/GaN quantum wells. The structure is grown by metal-organic vaporphase epitaxy. The photodetectors are fabricated using electron-beam lithography. The current–voltage characteristics exhibit a rectifying behavior. The spectral sensitivity of the photodetector is recorded starting from 3 eV and extending far in the UV range. The maximal photoresponse is observed at a wavelength of 367 nm (sensitivity 1.9 mA/W). The response switching time of the photodetector is less than 0.1 s.