Transparent crack-free samples of SrMoO4 single crystals are grown by using the Czochralski method. X-ray diffraction results confirmed a single phase of the grown crystals. Photoluminescence and X-ray-induced emission spectra showed a broad emission band in the wavelength range from 380 to 750 nm. The decay time curve contained two decay-time components of 0.7 ± 0.5 ns (20%) and 943 ± 50 ns (80%) at room temperature. Temperature dependences of the scintillation light yield and the decay time of the SrMoO4 crystal are also presented. Changes in the light yield and the decay time are observed at temperatures between 10 and 250 K. The light yield of SrMoO4 at 70 K is found to be three times higher than that at 250 K. The decay time of SrMoO4 get slower as the temperature decreases.