NbO _xmemristors show great application prospect in neuromorphic computing due to its nanoscale size, threshold switching, and locally active properties. The in-depth analysis and study of NbO _xmemristors’s dynamic properties are beneficial to the design and optimization of memristive neuron circuits. In this paper, based on the local active theory, the physical model of NbO _xmemristor is studied by using the small signal analysis method, and the region and conditions of the peak oscillation are quantitatively analyzed, and the quantitative relationship between the excitation signal amplitude and the peak frequency is determined. Based on the above theoretical analysis, NbO _xmemristor neurons are further designed and combined with the memristive synaptic crisscross array in order to construct a 25×10 spiking neural network (SNN). Finally, the recognitional function of digital 0 to 9 patterns is effectively realized by using frequency coding and time coding respectively.