A single crystalline Eu-doped GaN was grown by gas-source molecular beam epitaxy and photoluminescence properties were studied. The PL spectra show red-emission at 622 nm originating from intra 4f-4f transition of Eu3+ ion without band-edge emission of GaN. The peak shift of the red-emission with the temperature variation from 77 K to room temperature is 1.6 meV and thermal quenching of the luminescence was found to be very small for the same temperature range. A novel optical material whose emission wavelength and intensity are extremely stable with temperature was suggested.