The Green’s function technique and extended two sublattice pseudospin lattice coupled-mode (PLCM) model Hamiltonian have been applied to study the phase transition mechanism in $(NH_2CH_2COOH)_3H_2SO_4$ crystal. The two sublattice PLCM model Hamiltonian is modified by considering anharmonic phonon interactions, extra spin-lattice interactions, and an external applied electric field term. By using the double-time thermal-dependent Green function method along with PLCM model, the theoretical equations for the total shift, total width, normal mode frequency, transition temperature, relative permittivity, dielectric tangent loss, acoustic attenuation, spontaneous polarization and dielectric susceptibility are derived. By fitting the different values of model parameters in the theoretical obtained equations, we calculated the various temperature dependence properties such as normal (soft) mode frequency, relative permittivity, dielectric loss tangent, acoustic attenuation, spontaneous polarization and dielectric susceptibility. The theoretically obtained results are hold well and correlated with experimental data.