Abstract: A new SIS epidemic model with nonlinear incidence rate was proposed.Upon the consideration of vertical transmission,output and input of population,recruitment and natural mortality,the existence and stability of the disease-free equilibrium and the endemic equilibrium for the model were qualitatively analyzed and the limit cycles were also discussed.At last,the Bogdanov-Takens bifurcation was analyzed by carrying out a global qualitative method and the curves of saddle-node bifurcation,Hopf bifurcation and homoclinic bifurcation were obtained at the degenerate equilibrium.