Respiratory infection in humans and animals caused by influenza A viruses (IAV) is a severe economic and public health problem worldwide. Influenza virus will make the body’s innate immune signal activated during the early infection, which plays the role of defending, clearing the virus, and assisting the adaptive immune response. However, the influenza virus has developed a variety of escape strategies in the process of co-evolution with the host that mainly blocks the host’s innate immune pathway and inhibits the production of interferon and inflammatory factors through influenza virus self-proteins. We reviewed recent advances in host innate immune mechanisms against IAV infection and viral strategies for immune escaping, which may benefit the monitoring, target discovery, and vaccination development to prevent and control the influenza virus.