Spiking neural network,inspired by the human brain,consisting of spiking neurons and plastic synapses,is a promising solution for highly efficient data processing in neuromorphic computing.Recently,memristor-based neurons and synapses are becoming intriguing candidates to build spiking neural net-works in hardware,owing to the close resemblance between their device dynamics and the biological counterparts.However,the functionalities of memristor-based neurons are currently very limited,and a hardware demonstration of fully memristor-based spiking neural networks supporting in-situ learning is very challenging.Here,a hybrid spiking neuron combining a memristor with simple digital circuits is designed and implemented in hardware to enhance neuron functions.The hybrid neuron with memris-tive dynamics not only realizes the basic leaky integrate-and-fire neuron function but also enables the in-situ tuning of the connected synaptic weights.Finally,a fully hardware spiking neural network with the hybrid neurons and memristive synapses is experimentally demonstrated for the first time,and in-situ Hebbian learning is achieved with this network.This work opens up a way towards the implemen-tation of spiking neurons,supporting in-situ learning for future neuromorphic computing systems.