In this paper, hyper-Raman scattering intensities are calculated based on the quantum theory of radiation. From the intensity formulae, we can conclude directly that all Raman material that has vibration infra-red activity must have vibration hyper-Raman activity simultaneously. Because probability of dipole transition only contributes to anti-Stokes hyper-Raman scattering intensity, the intensity formulae of the anti-Stokes and Stokes are asymmetric, and the former consists of richer spectra than the latter. For the frequency shift of low wave number, the two intensities are almost identical even at room temperature. Finally, the resonance hyper-Raman scattering is also discussed.