SARS-CoV-2 infection causes complicated clinic manifestations with variable multi-organ injuries, however, the underlying mechanism, in particular immune responses in different organs, remains elusive. In this study, comprehensive transcriptomic alterations of 14 tissues from rhesus macaque infected with SARS-CoV-2 were analyzed. Compared to normal controls, SARS-CoV-2 infection resulted in dysregulation of genes involving diverse functions in various tissues/organs examined, with drastic transcriptomic changes in cerebral cortex and right ventricle. Intriguingly, cerebral cortex exhibited a hyperinflammatory state evidenced by significant upregulation of inflammation response-related genes. Meanwhile, expressions of coagulation, angiogenesis and fibrosis factors were also up-regulated in cerebral cortex. Neuronal receptor NRP1 expression showed a significant induction by SARS-CoV-2 in cerebral cortex, which might be responsible for a higher infectivity and consequent inflammatory response. Overall, our study depicts a multi-tissue/organ transcriptomic landscapes of rhesus macaque with early infection of SARS-CoV-2, and provides important insights into the mechanistic basis for COVID-19-associated clinical complications.