Inspired by the working modes of the human brain, the spiking neuron plays an important role as the basic computing unit of artificial perception systems and neuromorphic computing systems. However, the neuron circuit based on complementary metal-oxide-semiconductor technology has a complex structure, high power consumption, and limited flexibility. These features are not conducive to the large-scale integration and the application of flexible sensing systems compatible with the human body. The flexible memristor prepared in this work shows stable threshold switching characteristics and excellent mechanical bending characteristics with bending radius up to 1.5 mm and bending times up to 10 ⁴. The compact neuron circuit based on this device shows the key features of the neuron, such as threshold-driven spiking, all-or-nothing, refractory period, and strength-modulated frequency response. The frequency-input voltage relationship of the neuron shows the similarity of the rectified linear unit, which can be used to simulate the function of rectified linear unit in spiking neural networks. In addition, based on the electron transport mechanism, a core-shell model is introduced to analyze the working mechanism of the flexible memristor and explain the output characteristics of the neuron. In this model, the shell region consisting of Nb ₂O _5–xis subjected to ohmic conduction, while the core region consisting of NbO ₂is dominated by Poole-Frenkel conduction. These two mechanisms, combined with Newton’s law of cooling, dominate the threshold switching behavior of flexible memristor device. Furthermore, the threshold switching characteristic of the memristor is simulated, verifying the rationality of the working mechanism of the flexible memristor. Considering the fact that the threshold voltage decreases with temperature increasing, a correction term is added to the temperature of the shell region. Subsequently, the output characteristics of the neuron regulated by the input voltage are simulated. The simulation results show that the frequency increases but the threshold voltage decreases with the input voltage increasing, which is consistent with the experimental result. The introduction of the correction term confirms the influence of the thermal accumulation effect of the flexible substrate on neuron output characteristics. Finally, we build a spiking neural network based on memristive spiking neurons to implement handwriting recognition, achieving a 95.6% recognition rate, which is comparable to the ideal result of the artificial neural network (96%). This result shows the potential application of the memristive spiking neurons in neuromorphic computing. In this paper, the study of flexible neurons can guide the design of neuromorphic sensing and computing systems.