The statistical Green function theory and extended two sublattice pseudospin coupled-mode model Hamiltonian. The modified model summing with phonon anharmonic couplings, extra spin-lattice couplings, direct spin-spin coupling together with an applied electric field has been used to explain the dielectric properties of ammonium iron alum crystal. The expressions for energy shift, linewidth, ferroelectric soft mode frequency, dielectric permittivity, and dielectric loss tangent are derived. By fitted the model values of different parameters in the above theoretical expressions. The temperature dependence of soft mode frequency, dielectric permittivity, and dielectric loss properties have been numerically calculated. Our theoretical obtained results compared well agreement with experimental results reported by others.