Abstract: The initial-boundary value problems for a class of nonlinear nonlocal higher-order Kirchhoff partial differential equations is studied. Firstly, the existence and uniqueness of the global solution of the equation in space H_0^m + k(\Omega ) \times H_0^k(\Omega ) are proved by prior-estimation and Galerkin method. And then, the compact method is used to prove that the solution semigroup S(t) generated by the problem has a compact global attractor family A_k. Finally, the semigroup of operators is proved by linearization method. The Hausdorff dimension and Fractal dimension estimation of the global attractor family are obtained by using the Frechet differentiability and the attenuation of the volume element for the linearization problem.