As a highly pathogenic human coronavirus, SARS-CoV-2 has to counteract an intricate network of antiviral host responses to establish infection and spread. The nucleic acid-induced stress response is an essential component of antiviral defense and is closely related to antiviral innate immunity. However, whether SARS-CoV-2 regulates the stress response pathway to achieve immune evasion remains elusive. In this study, SARS-CoV-2 NSP5 and N protein were found to attenuate antiviral stress granule (avSG) formation. Moreover, NSP5 and N suppressed IFN expression induced by infection of Sendai virus or transfection of a synthetic mimic of dsRNA, poly (I:C), inhibiting TBK1 and IRF3 phosphorylation, and restraining the nuclear translocalization of IRF3. Furthermore, HEK293T cells with ectopic expression of NSP5 or N protein were less resistant to vesicular stomatitis virus infection. Mechanistically, NSP5 suppressed avSG formation and disrupted RIG-I-MAVS complex to attenuate the RIG-I-mediated antiviral immunity. In contrast to the multiple targets of NSP5, the N protein specifically targeted cofactors upstream of RIG-I. The N protein interacted with G3BP1 to prevent avSG formation and to keep the cofactors G3BP1 and PACT from activating RIG-I. Additionally, the N protein also affected the recognition of dsRNA by RIG-I. This study revealed the intimate correlation between SARS-CoV-2, the stress response, and innate antiviral immunity, shedding light on the pathogenic mechanism of COVID-19.