Gap junctions are the mechanism for striatal fast-spiking interneurons (FSIs) to interconnect with each other and play an important role in determining the physiological functioning of the FSIs. To investigate the effect of gap junctions on the firing activities and synchronization of the network for different external inputs, a simple network with least connections and a Newman-Watts small-world network were constructed. Our research shows that both properties of neural networks are related to the conductance of the gap junctions, as well as the frequency and correlation of the external inputs. The effect of gap junctions on the synchronization of network is different for inputs with different frequencies and correlations. The addition of gap junctions can promote the network synchrony in some conditions but suppress it in others, and they can inhibit the firing activities in most cases. Both the firing rate and synchronization of the network increase along with the increase of the electrical coupling strength for inputs with low frequency and high correlation. Thus, the network of coupled FSIs can act as a detector for synchronous synaptic input from cortex and thalamus.