The firing activity of a neuronal population is correlated, which has been linked to information coding and exchanging. Short-term synaptic plasticity allows synapses to increase (facilitate) or decrease (depress) over a wide range of time scales. It is critical to understand the characteristics and mechanisms of the correlated firing and the role of short-term synaptic plasticity in regulating firing activity. The short-term synaptic depression and facilitation are examined at the synapses in the inhibitory feedback loop of feedback neural networks. Numerical simulations reveal that the modulation of the correlated firing by dynamics of depression and facilitation is due to their effects on the synaptic strength. By varying synaptic time constants, the enhancement in either firing rate or intensity of oscillations can improve the correlated firing. Our study thus provides a general computational analysis of the sequential interaction of short-term plasticity with neuronal firing.