The synchronization in complete network consisting of  nodes is studied in this paper. Each node is connected to all other ones by nonlinear coupling and is represented by a reaction-diffusion system of FitzHugh-Nagumo type which can be obtained by simplifying the famous Hodgkin-Huxley model. From this complete network, the sufficient condition on the coupling strength to achieve the synchronization is found. The result shows that the networks with bigger in-degrees of nodes synchronize more easily. The paper also presents the numerical simulations for theoretical result and shows a compromise between the theoretical and numerical results.