Persistent irregular activity is defined as elevated irregular neural discharges in the brain in such a way that while the average network activity displays high frequency oscillations, the participating neurons display irregular and low frequency oscillations. This type of activity is observed in many brain regions like prefrontal cortex that plays a role in working memory. Previous studies have shown that large networks with sparse connections, networks with strong noise and persistent inhibition and networks with structured synaptic connections display persistent-irregular activity. However, experimental studies show that, not all brain regions obey these assumptions. In this study we show that a small network of excitatory–inhibitory neurons with random synaptic connections can reproduce persistent-irregular activity. In particular, the model shows that less than perfect rebound pattern in excitatory cells, coincident-sensitive inhibitory cells and sparse synaptic inhibition can account for persistent-irregular activity in an excitatory–inhibitory neural network with randomly assigned synaptic connections.