We study a non-linear mathematical model describing the transmission of Influenza virus A H1N1. The model is represented by a system of differential equations depending on parameters. Mathematical analysis shows that dynamics of the spread of the influenza virus is determined by the basic reproduction number R0. If R0 = 1, the disease free equilibrium is globally asymptotically stable, and if R0 > 1, the endemic equilibrium is globally asymptotically stable under some conditions. Lyapunov functional approach is used for proving the global stability of equilibria. A numerical investigation is carried out to confirmthe analytical results.