A theoretical description of the off-resonant coherent hyper-Raman scattering spectroscopy is presented. By considering two pump fields whose frequencies and corresponding wave vectors are omega(1), omega(2)(=2 omega(1)), k(1), and k(2), respectively, the effective Hamiltonian is derived to show that the spatial transient grating can be created by the third-order interaction with the pump fields. A delayed probe held with frequency of omega(1) and wave vector of k(1) is scattered by the spatial transient grating to produce the macroscopic polarization with wave vector 4k(1)-k(2). The expressions for the measured signals by homodyne and heterodyne method are derived and compared with that of the spontaneous hyper-Raman scattering signal.