We proposed a spiking neural network (SNN) learning algorithm using memristor-based inhibitory synapses to realize lateral inhibition and homeostasis in a compact way. Our proposed SNN has higher scalability and lower complexity by reducing connections and extra circuits to realize homeostasis. Software simulations on task of digital recognition of MNIST dataset showed that our proposed SNN learning algorithm can achieve a ~ 2X higher learning efficiency while maintaining comparable accuracy. The challenging imperfect properties of memristor, including limited conductance levels and intrinsic parameter variations are included in the simulation to verify the robustness of our proposed approach.