This paper is devoted to study the existence of global attractor in H01 (Ω) and uniform bounds of it in L∞(Ω) for a class of parabolic problems with homogeneous boundary conditions wich involves a uniform strongly elliptic operator of second order in the domain Ω ⊂ ℝn. The main tools used to prove the existence of global attractor are the techniques used in Hale [8] and Cholewa [5], and for the uniform bound of the attractor we use the Alikakos-Moser iteration procedure [1]. © 2014 NSP Natural Sciences Publishing Cor.