The growing number of reported avian influenza cases has prompted awareness of the importance of research methods to control the spread of the disease. Seasonal variation is one of the important factors that affect the spread of avian influenza. This paper presents a “nonautonomous” model to analyze the transmission dynamics of avian influenza with the effects of climate change. We obtain and discuss the global stability conditions of the disease-free equilibrium; the threshold conditions for persistence, permanence, and extinction of the disease; and the parameters with periodicity for controlling and eliminating the avian influenza.