We have developed a phonon-pseudospin coupled model in double-time Green's function theory to investigate dielectric properties of the ferroelectric strained superlattices BaTiO3/SrTiO3. We have calculated the influence of the phonon-pseudospin interaction on the dielectric susceptibility. The calculation results show that the peak of the dielectric susceptibility shifts up to higher temperature with increasing the pseudospin interaction, which means larger pseudospin interaction corresponds to higher transition temperature. As the phonon-pseudospin interaction is strengthened, the intensity and position of the susceptibility peak go up and shift to a higher temperature, respectively. The peak of the dielectric susceptibility shifts to a higher temperature with a rather high intensity when the BaTiO3/SrTiO3 superlattice period increases to a period 5/5, which is consistent with experimental results.