NbO_x memristors 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_x memristors’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_x memristor 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_x memristor 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.