In this paper the electrochemical impedance spectroscopy (EIS) method is applied through a transient in solid oxide fuel cell (SOFC) to obtain the dynamic modelling. Instead of measuring the current response of a fuel cell to a small sinusoidal perturbation in voltage at each frequency, the Hammerstein-Wiener model identification method is applied through a one transient who leads to the significant decrease of computational costs. Dynamic responses are determined as the solutions of coupled partial differential equations derived from conservation laws of charges, mass, momentum and energy with electrochemical kinetics by using Butler-Volmer model and gas diffusion on the extended Maxwell-Stefan species equations or dusty gas model (DGM). Because the system consisted of electrical and mechanical components, the behaviour of the system was nonlinear. The obtained results are in qualitative good agreement with experimental data published in literatures showed the effectiveness of the propose model. Finally a parametric study based on the obtained model is performed to study the effects of channel length, inlet H2 concentration, inlet velocity and cell temperature in Nyquist plots and the voltage responses to step changes in the fuel concentration and load current. The model can be useful as a benchmark for illustrating different designs and control schemes.