Cortical cortex is mainly composed of excitatory and inhibitory neurons. Balance between excitation and inhibition is a ubiquitous experimental phenomenon in brain. On the one hand, balanced excitation and inhibition plays a crucial role in maintaining normal brain functions; on the other hand, the loss of balance between the two opposing forces will cause neural diseases, such as epilepsy, Parkinson, schizophrenia, etc. Thus the research on balance between excitation and inhibition increasingly focuses on the field of neuroscience. Feedback neural circuit with recurrent excitatory and inhibitory connections is ubiquitous in cortical cortex. However, it is still little known how to achieve and maintain the balance between excitation and inhibition in feedback neural circuit. In this study it is proposed that inhibitory synaptic plasticity should play a key role in regulating the balance between excitation and inhibition. Firstly, the feedback neural circuit model is constructed using leaky integrate-and-fire neuron model, mainly composed of excitatory feed-forward loop, and excitatory and inhibitory recurrent connections. The proposed inhibitory synaptic model is incorporated into the feedback neural circuit model, and whose mathematical formulation is presented in detail. Secondly, the excitatory and inhibitory synaptic currents are obtained through numerical simulations, which demonstrate that the precise balance between excitation and inhibition is achieved under the regulation of inhibitory synaptic plasticity. Furthermore, the research results show that this balance is robust to the fluctuation inputs and disturbances. Thirdly, the balance mechanism underlined by inhibitory synaptic plasticity is elucidated through theoretical and simulation analysis, separately, which provides a clear explanation and an insight into how to achieve and maintain the balance between excitation and inhibition in a feedback neural circuit. Finally, the numerical results reveal that the neuron numbers in excitatory and inhibitory feedback loop exert an influence on the balance, and the larger number can enhance the balance between excitation and inhibition, which explains, to some extent, why there are dense connections between neurons in brain. The results in this study shed light on the balance mechanism of feedback neural circuit, and provide some clues for understanding the mechanism of balance between excitation and inhibition in the brain area.