This paper consider the long time behavior of a class of nonlinear damped Kirchhoff equation    2 tt 1 t t u u u u u f x          . Study the attractor problem with initial boundary value conditions, then using priori estimate and the Galerkin method prove existence and uniqueness of solution, we obtain to the existence of the global attractors. The squeezing property of the nonlinear semi-group associated with this equation and the existence of exponential attractors are also proved.