In this paper, we present an electrical circuit of a leaky integrate-and-fire neuron with one VO2 switch, which models the properties of biological neurons. Based on VO2 neurons, a two-layer spiking neural network consisting of nine input and three output neurons is modeled in the SPICE simulator. The network contains excitatory and inhibitory couplings, and implements the winner-takes-all principle in pattern recognition. Using a supervised Spike-Timing-Dependent Plasticity training method and a timing method of information coding, the network was trained to recognize three patterns with dimensions of 3 × 3 pixels. The neural network is able to recognize up to 105 images per second, and has the potential to increase the recognition speed further.