Through the research on the fractional-order FitzHugh-Nagumo model neuron，it is found that the Hopf bifurcation point of the fractional-order model，where the state of the model neuron changes from quiescence to periodic spiking，is different from that of the corresponding integer-order model when the externally applied current is considered as the bifurcation parameter. We further demonstrate that the range of the strength of the externally applied current in the fractional-order model neuron，which can make the model neuron exhibit periodic spiking，is smaller than that in the corresponding integer-order model neuron. However，the firing frequency of the fractional-order model neuron is higher than that of the integer-order counterpart. Meanwhile，we show that the synchronization rate of two electrically coupled fractional-order FitzHugh-Nagumo model neurons is greater than that of the integer-order counterpart. The Adomian decomposition method is employed to calculate fractional-order differential equations numerically because of its rapid convergence and high accuracy.