The newly identified Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has resulted in a global health emergency (COVID-19) because of its rapid spread and high mortality. Since the virus epidemic, many pathogenic mechanisms have been revealed, and virus-related vaccines have been successfully developed and applied in clinical practice. However, the pandemic is still developing, and new mutations are still emerging. Virus pathogenicity is closely related to the immune status of the host. As innate immunity is the body’s first defense against viruses, understanding the inhibitory effect of SARS-CoV-2 on innate immunity is of great significance for determining the target of antiviral intervention. This review summarizes the molecular mechanism by which SARS-CoV-2 escapes the host immune system, including suppressing innate immune production and blocking adaptive immune priming. Here, on the one hand, we devoted ourselves to summarizing the combined action of innate immune cells, cytokines, and chemokines to fine-tune the outcome of SARS-CoV-2 infection and the related immunopathogenesis. On the other hand, we focused on the effects of the SARS-CoV-2 on innate immunity, including enhancing viral adhesion, increasing the rate of virus invasion, inhibiting the transcription and translation of immune-related mRNA, increasing cellular mRNA degradation, and inhibiting protein transmembrane transport. This review on the underlying mechanism should provide theoretical support for developing future molecular targeted drugs against SARS-CoV-2. Nevertheless, SARS-CoV-2 is a completely new virus, and people’s understanding of it is in the process of rapid growth, and various new studies are also being carried out. Although we strive to make our review as inclusive as possible, there may still be incompleteness.