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<p>Abstract</p> <p>The long-time behavior of solution to extended Fisher-Kolmogorov equation is considered in this article. Using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor, we prove that the extended Fisher-Kolmogorov equation possesses a global attractor in Sobolev space <it>H^k</it>for all <it>k </it>&gt; 0, which attracts any bounded subset of <it>H^k </it>(&#937;) in the <it>H^k </it>-norm.</p> <p><b>2000 Mathematics Subject Classification: </b>35B40; 35B41; 35K25; 35K30.</p>