The newly emerging coronavirus SARS-CoV-2 causes severe lung disease and substantial mortality. How the virus evades host defense for efficient replication is not fully understood. In this report, we found that the SARS-CoV-2 nucleocapsid protein (NP) impaired stress granule (SG) formation induced by viral RNA. SARS-CoV-2 NP associated with the protein kinase PKR after dsRNA stimulation. SARS-CoV-2 NP did not affect dsRNA-induced PKR oligomerization, but impaired dsRNA-induced PKR phosphorylation (a hallmark of its activation) as well as SG formation. SARS-CoV-2 NP also targeted the SG-nucleating protein G3BP1 and impaired G3BP1-mediated SG formation. Deficiency of PKR or G3BP1 impaired dsRNA-triggered SG formation and increased SARS-CoV-2 replication. The NP of SARS-CoV also targeted both PKR and G3BP1 to impair dsRNA-induced SG formation, whereas the NP of MERS-CoV targeted PKR, but not G3BP1 for the impairment. Our findings suggest that SARS-CoV-2 NP promotes viral replication by impairing formation of antiviral SGs, and reveal a conserved mechanism on evasion of host antiviral responses by highly pathogenic human betacoronaviruses.