In this paper, our study on the hydrogen-bond ferroelectrics with Green's function method is reviewed. First we show how to apply the bose-type Green's function method properly to the pseudo-spin model. Then we introduce the four-body interaction in the pseudo-spin model in order to treat the first order phase transition. Analysing the equation describing the phase transition process, we propose a new condition to determine the nature of the system. Also we obtain the critical value of the model parameters and the phase diagram. Our conclusion is that the first order phase transition is induced by the fourbody interaction.