Inverse Chaotic Resonance (ICR) refers to the phenomenon in which the mean firing rate is reduced with an optimal intensity of the chaotic activity. In this study, ICR is numerically investigated by modeling the scale-free network topology of Hodgkin-Huxley neurons coupled electrical, excitatory, and inhibitory chemical synapses. First, it is shown that chaotic signals play an important role in changing the average firing frequency of the network consisting of neurons connected by any synaptic coupling. Then it is expressed that the ICR phenomenon occurs depending on the synaptic strength and that even double ICR behavior can also emerge at two different optimal epsilon levels in the case of inhibitory synapse. Moreover, ICR can be modulated by a constant stimulus, and this phenomenon covers a wider range of chaotic current densities at a constant current level close to the excitation threshold. In addition, the effects of the synaptic time constant and network inputs on the appearance of the phenomenon are also examined. These extensive numerical results suggest a new perspective on ICR effect is a robust phenomenon that is observed in neuronal networks regardless of their topological structure.