Based on biological experimental data, we developed a mathematical model of the virus-triggered signaling pathways that lead to induction of type I IFNs and systematically analyzed the mechanisms of the cellular antiviral innate immune responses, including the negative feedback regulation of ISG56 and the positive feedback regulation of IFNs. We found that the time between 5 and 48 hours after viral infection is vital for the control and/or elimination of the virus from the host cells and demonstrated that the ISG56-induced inhibition of MITA activation is stronger than the ISG56-induced inhibition of TBK1 activation. The global parameter sensitivity analysis suggests that the positive feedback regulation of IFNs is very important in the innate antiviral system. Furthermore, the robustness of the innate immune signaling network was demonstrated using a new robustness index. These results can help us understand the mechanisms of the virus-induced innate immune response at a system level and provide instruction for further biological experiments.