The avian influenza A (H7N9) virus is one subtype of influenza viruses, which has previously been isolated only in birds. Recently, an outbreak of a new avian influenza (H7N9) in China has resulted in numerous infections and high mortality in the humans. The H7N9 virus is low pathogenic in poultry and high pathogenic in human and that is critically different from other avian influenza viruses. An increasing number of the new H7N9 cases and the high mortality have caused a serious global concern. Here, based on the reported data, we propose and analyze an SE-SEIS avian–human influenza model. We prove the global stability results for both the disease-free equilibrium point and the endemic equilibrium point by using a general Bendixson–Dulac theorem. Our reported theoretical results of this paper are expected to help in exploring the development of efficient methods to controlling the spread of avian influenza A(H7N9).