We study the existence of the (L-2(R), W-1,W-p(R))-global attractor for an evolution p-Laplacian equation. Under additional restrictions on force and source terms we improve the result of [A. Kh. Khanmamedov, Existence of a global attractor for the parabolic equation with nonlinear Laplacian principal part in an unbounded domain, J. Math. Anal. Appl. 316 (2006) 601-615] and correct the result of [M. Yang, C. Sun, C. Zhong, Existence of a global attractor for a p-Laplacian equation in R-n, Nonlinear Anal. 66 (2007) 1-13] in the one dimensional case. (C) 2008 Elsevier Ltd. All rights reserved.