The dynamics of a class of autonomous impulsive differential equation was studied,and the sufficient conditions for the existence and stability of a semi-trivial periodic solution were obtained.The problem of periodic solution was transformed into a fixed-point problem by constructing the Poncaré map.Theoretical analysis and numerical results show that a steady positive period-1 solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. And the numerical results also show that,when the control parameter varies, a positive period-2 solution bifurcates from the positive periodic solution through a flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations.