article studies the influence of the small delays on the FitzHugh-Nagumo network synchronization. It is widely known that high delays in signal propagation between the nodes make synchronization difficult or even impossible. The sufficient conditions of the linearized network synchronization for the case of the small delay are obtained. This problem is successfully reduced to the feasibility of the LMIs. The simulation results confirm the efficiency of the obtained conditions. We suppose that the similar conditions can be applicable even to the nonlinear FitzHugh-Nagumo network.