Neural firing rate homeostasis, as an important feature of neural electrical activity, means that the firing rate in brain is maintained in a relatively stable state, and fluctuates around a constant value. Extensive experimental studies have revealed that the firing rate homeostasis is ubiquitous in brain, and provides a base for neural information processing and maintaining normal neurological functions, so that the research on neural firing rate homeostasis is a central problem in the field of neuroscience. Cortical neural network is a highly complex dynamic system with a large number of input disturbance signals and parameter perturbations due to dynamic connection. However, it remains to be further investigated how firing rate homeostasis is established in cortical neural network, furthermore, maintains robustness to these disturbances and perturbations. The feedback neural circuit with recurrent excitatory and inhibitory connection is a typical connective pattern in cortical cortex, and inhibitory synaptic plasticity plays a crucial role in achieving neural firing rate homeostasis. Here, by constructing a feedback neural network with inhibitory spike timing-dependent plasticity (STDP), we conduct a computational research to elucidate the mechanism of neural firing rate homeostasis. The results indicate that the neuronal firing rate can track the target firing rate accurately under the regulation of inhibitory synaptic plasticity, thus achieve firing rate homeostasis. In the face of external disturbances and parameter perturbations, the neuron firing rate deviates transiently from the target firing rate value, and converges to the target firing rate value at a steady state, which demonstrates that the firing rate homeostasis established by the inhibitory synaptic plasticity can maintain strong robustness. Furthermore, the analytical research qualitatively explains the firing rate homeostasis mechanism underlined by inhibitory synaptic plasticity. Finally, the simulations further demonstrate that the learning rate value and the firing rate set point value also exert a quantitative influence on the firing rate homeostasis. Overall, these findings not only gain an insight into the firing rate homeostasis mechanism underlined by inhibitory synaptic plasticity, but also inspire testable hypotheses for future experimental studies.