The collision-induced rototranslational hyper-Rayleigh spectra of gaseous H(2)-He mixture are computed and discussed in the binary regime. As the input data we use our ab initio computed H(2)-He collision-induced first dipole hyperpolarizability tensor Deltabeta(R). Both the vector and the septor part of the H(2)-He hyper-Rayleigh spectra are evaluated at room temperature (T=295 K). The spectra are calculated assuming the full quantum computations based on the Schrödinger equation of the relative translational motion in the isotropic H(2)-He potential as well as using semiclassical methods.